The present invention relates to methods of using G-matrix Fourier transformation nuclear magnetic resonance (GFT NMR) spectroscopy for rapidly obtaining and connecting precise chemical shift values and determining the structure of proteins and other molecules.
Nuclear magnetic resonance (NMR) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Wxc3xcthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996))-based structural studies rely on two broad classes of experimental radio-frequency pulse schemes for recording two-dimensional (2D) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987)), three-dimensional (3D) (Oschkinat et al., Nature, 332:374-376 (1988)), or four-dimensional (4D) (Kay et al., Science, 249:411-414 (1990)) Fourier transformation (FT) NMR spectra. Correlation spectroscopy (COSY) delineates exclusively scalar coupling connectivities to measure chemical shifts, and (heteronuclear resolved) 1H, 1H-nuclear Overhauser enhancement spectroscopy (NOESY) reveals the strength of through-space dipolar couplings of 1H spins to estimate distances (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Wxc3xcthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986)). NMR spectra need to exhibit (i) signal-to-noise (S/N) ratios warranting reliable data interpretation, (ii) digital resolutions ensuring adequate precision for the measurement of NMR parameters such as chemical shifts, and (iii) a dimensionality at which a sufficient number of NMR parameters is correlated (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)). While increased intensity of NOESY peaks ensures their more accurate integration (which, in turn, may translate into increased accuracy of the NMR structure), the mere identification of COSY peaks suffices to obtain the desired chemical shifts. Hence, COSY peak signal-to noise ratios larger that xcx9c3:1 reflect, in essence, inappropriately long measurement times. Moreover, the total number of peaks in COSY grows only linearly with the number of spins involved and is, for a defined magnetization transfer pathway, xe2x80x9cindependentxe2x80x9d of the dimensionality N. Thus, a minimal xe2x80x9ctarget dimensionalityxe2x80x9d Nt at which most of the COSY peaks detected for a given molecule are resolved can be defined. Further increased dimensionality does not aim at resolving peak overlap but at increasing the number of correlations obtained in a single data set. This eliminates ambiguities when several multidimensional NMR spectra are combined for resonance assignment, for example, when using 1H, 13C, 15N triple-resonance NMR to assign protein resonances (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)).
An increase in dimensionality is, however, limited by the need to independently sample the indirect dimensions, because this leads to longer measurement times. Although the measurement time can be somewhat reduced by aliasing signals (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)) or accepting a lower digital resolution in the indirect dimensions, high dimensionality often prevents one from tuning the measurement time to a value that ensures to obtain sufficient, but not unnecessarily large S/N ratios.
In view of these considerations, xe2x80x9csamplingxe2x80x9d and xe2x80x9csensitivity limitedxe2x80x9d data collection regimes are defined (Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002)), depending on whether the sampling of the indirect dimensions or the sensitivity of the FT NMR experiment determines the minimal measurement time. In the sensitivity limited regime, long measurement times are required to achieve sufficient S/N ratios, so that the sampling of indirect dimensions is not necessarily constraining the adjustment of the measurement time. In the sampling limited regime, some or even most of the instrument time is invested for sampling, which yields excessively large S/N ratios. In view of the ever increasing sensitivity of NMR instrumentation, new methodology to avoid the sampling limited regime is needed. (Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002)).
In general, phase-sensitive acquisition of an N-dimensional (ND) FT NMR experiment (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987); Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)) requires sampling of Nxe2x88x921 indirect dimensions with n1xc3x97n2 . . . nNxe2x88x921 complex points representing       n    FID    =            2              N        -        1              ·                  ∏                  j          =          1                          N          -          1                    ⁢              xe2x80x83            ⁢              n        j            
free induction decays (FIDs). The resulting steep increase of the minimal measurement time, Tm, with dimensionality prevents one from recording five- or higher-dimensional FT NMR spectra: acquiring 16 complex points in each indirect dimension (with one scan per FID each second) yields Tm(3D)=0.5 hour, Tm(4D)=9.1 hours, Tm(5D)=12 days, and Tm(6D)=1.1 years.
Thus, higher-dimensional FT NMR spectroscopy suffers from two major drawbacks: (i) The minimal measurement time of an ND FT NMR experiment, which is constrained by the need to sample Nxe2x88x921 indirect dimensions, may exceed by far the measurement time required to achieve sufficient signal-to-noise ratios. (ii) The low resolution in the indirect dimensions severely limits the precision of the indirect chemical shift measurements.
The present invention is directed to overcoming the deficiencies in the art.
The present invention relates to a method of conducting a (N,Nxe2x88x92K) dimensional (D) G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiment, where N is the dimensionality of an N-dimensional (ND) Fourier transformation (FT) NMR experiment and K is the desired reduction in dimensionality relative to N. The method involves providing a sample and applying radiofrequency pulses for the ND FT NMR experiment to the sample. Then, m indirect chemical shift evolution periods of the ND FT NMR experiment are selected, where m equals K+1, and the m indirect chemical shift evolution periods are jointly sampled. Next, NMR signals detected in a direct dimension are independently cosine and sine modulated to generate (Nxe2x88x92K)D basic NMR spectra containing frequency domain signals with 2K chemical shift multiplet components, thereby enabling phase-sensitive sampling of all jointly sampled m indirect chemical shift evolution periods. Finally, the (Nxe2x88x92K) D basic NMR spectra are transformed into (Nxe2x88x92K) D phase-sensitively edited basic NMR spectra, where the 2K chemical shift multiplet components of the (Nxe2x88x92K) D basic NMR spectra are edited to yield (Nxe2x88x92K) D phase-sensitively edited basic NMR spectra having individual chemical shift multiplet components.
Another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an xcex1-proton, 1Hxcex1, an xcex1-carbon, 13Cxcex1, a polypeptide backbone carbonyl carbon, 13Cxe2x80x2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1HN, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,2)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921, the xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi and (2) a (5,2)D [HACA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921. Then, sequential assignments of the chemical shift values of 1Hxcex1, 13Cxcex1, 13Cxe2x80x2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,2)D [HACACONHN] GFT NMR experiment with the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,2)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.
Yet another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an xcex1-proton, 1Hxcex1, an xcex1-carbon, 13Cxcex1, a polypeptide backbone carbonyl carbon, 13Cxe2x80x2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1HN, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921, the xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi and (2) a (5,3)D [HACA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921. Then, sequential assignments of the chemical shift values of 1Hxcex1, 13Cxcex1, 13Cxe2x80x2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,3)D [HACACONHN] GFT NMR experiment with the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,3)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.
A further aspect of the present invention relates to a method for sequentially assigning chemical shift values of xcex1- and xcex2-carbons, 13Cxcex1/xcex2, a polypeptide backbone carbonyl carbon, 13Cxe2x80x2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1HN, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [CBCACONHN] GFT NMR experiment to measure and connect the chemical shift values of the xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, the polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi and (2) a (4,3)D [CBCA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of 13Cxcex1/xcex2ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921. Then, sequential assignments of the chemical shift values of 13Cxcex1/xcex2, 13Cxe2x80x2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 and 13Cxe2x80x2ixe2x88x921 measured by the (4,3)D [CBCACONHN] GFT NMR experiment with the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 and 13Cxe2x80x2ixe2x88x921 measured by the (4,3)D [CBCA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of 13Cxcex1/xcex2ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.
The present invention also relates to a method for sequentially assigning chemical shift values of xcex1- and xcex2-carbons, 13Cxcex1/xcex2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1HN, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [HNNCACBCA] GFT NMR experiment to measure and connect the chemical shift values of the xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, the xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921 and (2) a GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi. Then, sequential assignments of the chemical shift values of 13Cxcex1/xcex2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 measured by the GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment with the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 measured by the (4,3)D [HNNCACBCA] GFT NMR experiment, (ii) using the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921, and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements within the polypeptide chain.
Another aspect of the present invention relates to a method for assigning chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain protons, 1Hxcex3/xcex4/xcex5, and chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain carbons located peripheral to xcex2-carbons, 13Cxcex3/xcex4/xcex5, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue ixe2x88x921, 1Hixe2x88x921, a carbon of amino acid residue ixe2x88x921 coupled to 1Hixe2x88x921, 13Cixe2x88x921, a carbon coupled to 13Cixe2x88x921, 13Cixe2x88x921coupled, and a proton coupled to 13Cixe2x88x921coupled, 1Hixe2x88x921coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of xcex1- and xcex2-protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921, and xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921. Then, assignments of the chemical shift values of 1Hxcex3/xcex4/xcex5 and 13Cxcex3/xcex4/xcex5 are obtained by (i) identifying 1Hixe2x88x921, 13Cixe2x88x921, 13Cixe2x88x921coupled, and 1Hixe2x88x921coupled measured by the (5,3)D [HCC,CH-COSY] GFT NMR experiment as 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxcex2ixe2x88x921, and 1Hxcex2ixe2x88x921, respectively, and thereby matching the chemical shift values of 1Hxcex1/xcex2ixe2x88x921, and 13Cxcex1/xcex2ixe2x88x921 with the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 in conjunction with other chemical shift connections from the (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure the chemical shift values of 1Hxcex3/xcex4/xcex5ixe2x88x921 and 13Cxcex3/xcex4/xcex5ixe2x88x921.
Yet another aspect of the present invention relates to a method for assigning chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain protons, 1Hxcex3/xcex4/xcex5, and chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain carbons located peripheral to xcex2-carbons, 13Cxcex3/xcex4/xcex5, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,2)D [HCCH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue ixe2x88x921, 1Hixe2x88x921, a carbon of amino acid residue ixe2x88x921 coupled to 1Hixe2x88x921, 13Cixe2x88x921, a carbon coupled to 13Cixe2x88x921, 13Cixe2x88x921coupled, and a proton coupled to 13Cixe2x88x921coupled, 1Hixe2x88x921coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of xcex1- and xcex2-protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921, and xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921. Then, assignments of the chemical shift values of 1Hxcex3/xcex4/xcex5 and 13Cxcex3/xcex4/xcex5 are obtained by (i) identifying 1Hixe2x88x921, 13Cixe2x88x921, 13Cixe2x88x921coupled, and 1HNixe2x88x921coupled measured by the (4,2)D [HCCH-COSY] GFT NMR experiment as 1Hxcex1ixe2x88x921, Cxcex1ixe2x88x921, 13Cxcex2ixe2x88x921, and 1Hxcex2ixe2x88x921 respectively, and thereby matching the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 with the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 in conjunction with other chemical shift connections from the (4,2)D [HCCH-COSY] GFT NMR experiment to measure the chemical shift values of 1Hxcex3/xcex4/xcex5ixe2x88x921 and 3Cxcex3/xcex4/xcex5ixe2x88x921.
A further aspect of the present invention relates to a method for assigning chemical shift values of a xcex3-carbon, 13Cxcex3, a xcex4-carbon, 13Cxcex4, and a xcex4-proton, 1Hxcex4, of an amino acid residue containing an aromatic spin system in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HBCBCGCDHD] GFT NMR experiment to measure and connect the chemical shift values of a xcex2-proton of amino acid residue ixe2x88x921, 1Hxcex2ixe2x88x921, a xcex2-carbon of amino acid residue ixe2x88x921, 13Cxcex2ixe2x88x921, a xcex3-carbon of amino acid residue ixe2x88x921, 13Cxcex3ixe2x88x921, a xcex4-carbon of amino acid residue ixe2x88x921, 13Cxcex4ixe2x88x921, and a xcex4-proton of amino acid residue ixe2x88x921, 1Hxcex4ixe2x88x921, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of 1Hxcex2ixe2x88x921 and 13Cxcex2ixe2x88x921. Then, assignments of the chemical shift values of 13Cxcex3, 13Cxcex4, and 1Hxcex4 are obtained by (i) matching the chemical shift values of 1Hxcex2ixe2x88x921 and 13Cxcex2ixe2x88x921 measured by the (5,3)D HBCBCACA(CO)NHN GFT NMR experiment with the chemical shift values of 1Hxcex2ixe2x88x921 and 13Cxcex2ixe2x88x921, measured by the (5,3)D [HBCBCGCDHD] GFT NMR experiment, and (ii) using the chemical shift values of 13Cxcex3, 13Cxcex4, and 1Hxcex4 to identify the type of amino acid residue containing the aromatic spin system.
The present invention also relates to a method for assigning chemical shift values of aliphatic and aromatic protons and aliphatic and aromatic carbons of an amino acid residue containing aliphatic and aromatic spin systems in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a first GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aliphatic spin system, to measure and connect the chemical shift values of xcex1- and xcex2-protons of amino acid residue i, 1Hxcex1/xcex2i, xcex1- and xcex2-carbons of amino acid residue i, 13Cxcex1/xcex2i, a xcex4-carbon of amino acid residue i, 13Cxcex3i, and (2) a second GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aromatic spin system, to measure and connect the chemical shift values of 13Cxcex3i and other aromatic protons and carbons of amino acid residue i. Then, assignments of the chemical shift values of the aliphatic and aromatic protons and aliphatic and aromatic carbons are obtained by matching the chemical shift value of 13Cxcex3i measured by the first GFT NMR experiment with the chemical shift value of 13Cxcex3i measured by the second GFT NMR experiment.
Another aspect of the present invention relates to a method for obtaining assignments of chemical shift values of 1H, 13C, and 15N of a protein molecule. The method involves providing a protein sample and conducting five G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample, where (1) a first experiment is a (4,3)D [HNNCACBCA] GFT NMR experiment for obtaining intraresidue correlations of chemical shift values; (2) a second experiment is a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment for obtaining interresidue correlations of chemical shift values; (3) a third experiment is a (5,3)D [HCC,CH-COSY] GFT NMR experiment for obtaining assignments of aliphatic sidechain chemical shift values; (4) a fourth experiment is a (5,3)D [HBCBCGCDHD] GFT NMR experiment for linking chemical shift values of aliphatic protons, 1Hxcex2 and 13Cxcex2, and aromatic protons, 13Cxcex4 and 1Hxcex4; and (5) a fifth experiment is a (4,2)D [HCCH-COSY] GFT NMR experiment for obtaining assignments of aromatic sidechain chemical shift values.
The present invention discloses a number of specific GFT NMR experiments and different combinations of those experiments which allows one to obtain sequential backbone chemical shift assignments for determining the secondary structure of a protein molecule and complete assignments of chemical shift values for a protein molecule including aliphatic and aromatic sidechain spin systems.
The present invention provides a generally applicable approach for NMR data acquisition and processing named xe2x80x9cGFT NMR spectroscopyxe2x80x9d. This approach is based on the phase-sensitive joint sampling of several indirect dimensions while ensuring that all chemical shift correlations are retained. The employment of GFT NMR focuses on the sampling limited data collection regime and, considering that NMR measurements longer than about a week are impracticable, on the acquisition of five- or higher-dimensional spectral information.
GFT NMR relaxes on constraints arising from two major drawbacks of FT NMR, that is, the problem of having excessive or prohibitively long measurement times due to sampling of indirect dimensions and the limited precision of chemical shift measurements in the indirect dimensions arising from comparably low digital resolution. Within a few hours or less, GFT NMR spectroscopy affords the correlations of even five- or higher-dimensional FT NMR spectra acquired with high digital resolution. Thus, GFT NMR spectroscopy allows one to tune measurement times to sensitivity requirements without compromising on the dimensionality or the digital resolution. High-throughput efforts such as NMR-based structural genomics (Montelione et al., Nat. Struct. Biol., 7:982-984 (2000), which is hereby incorporated by reference in its entirety) will profit from this feature, because automated resonance assignment (Szyperski et al., J. Biomol. NMR, 11:387-405 (1998); Moseley et al, Curr. Opin. Struct. Biol., 9:635-642 (1999); Moseley et al., Methods Enzymol., 339:91-108 (2001), which are hereby incorporated by reference in their entirety) benefits from maximizing the number of correlations obtained from in a single NMR experiment. Moreover, the rapid sampling realized with GFT NMR spectroscopy will allow researchers to obtain highest dimensional NMR information with exceptional time resolution when, for example, studying slow protein folding in real time (Dyson et al., Annu. Rev. Phys. Chem., 47:369-395 (1996), which is hereby incorporated by reference in its entirety). The high precision of the chemical shift measurements is of potential importance for a broad range of NMR applications in natural sciences and engineering, for example, for automated assignment, or when studying systems with high chemical shift degeneracy such as RNA ribose spin systems (Cromsigt et al., Methods Enzymol., 338:371-399 (2001), which is hereby incorporated by reference in its entirety), (partially) unfolded proteins (Neri et al., FEBS Lett., 303:129-135 (1992), which is hereby incorporated by reference in it its entirety), or lipids (Wang et al., Biochemistry, 41:5453-5461 (2002), which is hereby incorporated by reference in its entirety). Finally, the high precision of the shift measurements may be recruited to accurately measure other NMR parameters such as residual dipolar couplings for structural refinement (Tjandra et al., Science, 278:1111-1114 (1997); Prestegard, Nat. Struct. Biol., 5:517-522 (1998), which are hereby incorporated by reference in their entirety), and transverse relaxation optimized (Pervushin et al., Proc. Natl. Acad. Sci. USA, 94:12366-12371 (1997), which is hereby incorporated by reference in its entirety) GFT NMR may develop into a powerful approach to investigate larger systems.
In the sensitivity limited regime, GFT NMR may be advantageous in cases where an extended radiofrequency (rf) phase cycle is desirable for spectral editing and/or improved artifact suppression (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety).
FIG. 1 compares the conventional sampling of a 3D time domain subspace of an ND FT NMR experiment (on the left) with the phase-sensitive joint sampling of the three dimensions in an (N,N-2)D GFT NMR (on the right), that is, with K=2. Processing of the FT NMR experiment requires a 3D FT of the subspace, while the GFT NMR experiment requires time domain editing of chemical shift multiplet components by application of the so-called G-matrix (see equation 1 in the xe2x80x9cDetailed Description of the Inventionxe2x80x9d) and ID FT of the resulting p=2K+1 data sets. For the GFT NMR experiment, the phase settings of xc3x81 and xc3x82 of the rf pulses creating transverse magnetization for frequency labeling with xcexa91 and xcexa92 are indicated for basic spectra (top four rows), first-order central peak spectra (two rows in the middle), and the second-order central peak spectrum (bottom row). Instead of a single peak in FT NMR which encodes three chemical shifts, one obtains a p-fold overdetermined system of equations. A least-squares fit calculation yields the three shifts from the position of seven peaks. In a GFT NMR experiment with constant-time chemical shift evolution periods, the lines forming the chemical shift multiplets have the same width as the resonances in FT NMR (if recorded with corresponding maximal evolution times; see also FIGS. 18A-B). (The width at half height of the frequency domain sinc centre lobe resulting from truncation in the time domain at tmax is given (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) by 0.604/tmax. In the current implementation of (5,2)D HACACONHN (FIG. 6) all indirect evolution periods except for xcexa9(1Hxcex1) are constant-time periods. The evolution of xcexa9(1Hxcex1) is implemented in a semiconstant-time manner (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety), so that signal losses due to transverse relaxation of 1Hxcex1 are negligible for 8.6 kDa ubiquitin at short tmax values around 6.5 ms. For larger systems with short T2(1Hxcex1), however, the semiconstant-time frequency labeling may lead to a detectable increase of xcfx891-line widths in the basic when compared to central peak spectra.) This yields the same standard deviation xcex94xcexa9 for the identification of peak positions in the two experiments. Hence, the standard deviation of the chemical shift measurements obtained xe2x80x9cafterxe2x80x9d the least-squares fit is reduced (Eadie et al., Statistical Methods in Experimental Physics, North-Holland, N.Y. (1982), which is hereby incorporated by reference in its entirety) by a factor 1/√{square root over (n)} in GFT NMR. For simplicity, it is assumed that the n peaks which contribute to the calculation of a given shift exhibit the same line widths (see descriptions of FIGS. 19-20).
FIGS. 2A-D show a stick diagram exemplifying the formation of chemical shift multiplets (on the left) for K=3 and phase-sensitively edited multiplet components (on the right) in the frequency domain. FIG. 2A shows the basic spectra yielding the following linear combinations: B1 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8; B2 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8; B3 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8; B4 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8; B5 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8; B6 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8; B7 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8; B8 [xcexa90+xcexa91+xcexa92+xcexa93]=A1+A2+A3+A4+A5+A6+A7+A8. FIG. 2B shows the first order central peak spectra: B9 [xcexa90+xcexa91+xcexa92]=A9+A10+A11+A12; B10 [xcexa90xe2x88x92xcexa91+xcexa92]=A9xe2x88x92A10+A11xe2x88x92A12; B11 [xcexa90+xcexa91xe2x88x92xcexa92]=A9+A10xe2x88x92A11xe2x88x92A12; B12 [xcexa90xe2x88x92xcexa91xe2x88x92xcexa92]=A9xe2x88x92A10xe2x88x92A11+A12. FIG. 2C shows the second order centralpeak spectra: B13 [xcexa90+xcexa91]=A13+A14; B14 [xcexa90xe2x88x92xcexa91]=A13xe2x88x92A14. FIG. 2D shows the third order central peak spectra: B15=A15. For the calculation of the matrices F(K), see Example 1. To facilitate the comparison of the left and the right section the positions of multiplet components are indicated with thin lines.
FIGS. 3A-B illustrate the xe2x80x9cbottom-upxe2x80x9d identification of the peaks forming a chemical shift multiplet in GFT NMR, provided that three indirect dimensions of a FT NMR experiment are jointly sampled (FIG. 1; K=2). FIG. 3A shows that two spin systems exhibiting degenerate chemical shifts in all other conventionally sampled Ntxe2x88x921 dimensions give rise to basic, first order central and second order central peaks shown in bold (spin system 1) and lighter shade (spin system 2), respectively. Knowledge of the position of the second order central peak of spin system 1 allows identification of the corresponding first order central peaks of spin system 1. In turn, their knowledge allows unambiguous identification of the corresponding peaks of spin system 1 in the basic spectra. As indicated by the dashed line on the left in FIG. 3A, the peaks in B1 and B3 (shown in bold) are centered around the peak in B5 (shown in bold), while, as indicated by the dashed line on the right in FIG. 3A, the peaks in B2 and B4 (shown in bold) are centered around the peak in B5 (shown in bold). This strategy can readily be extended for K greater than 2. In practice, the identification of components belonging to a given shift multiplets is greatly facilitated by inspection of peak intensities: the components forming a given multiplet are expected to exhibit (nearly) the same intensity. To illustrate this point, the resonance lines of spin system 2 were assumed to be more intense than those of spin system 1. FIG. 3B shows that, in addition to chemical shift degeneracy in the conventionally sampled Ntxe2x88x921 dimensions, the central peaks of spin system 1 (as described in FIG. 3A) and those of spin system 3 (peaks shown in lighter shade) overlap. In this case, the two spin systems exhibit degenerate chemical shifts in all but one dimension of an ND FT NMR spectrum. In (N,Nt)D GFT NMR, the bottom-up identification of multiplet components resolves and groups the signals of the two spin systems in the basic spectra, thus yielding the equivalent of the ND chemical shift correlation.
FIGS. 4A-C illustrate magnetization transfer pathways of the following GFT NMR experiments: (5,2)D HACACONHN and (5,2)D HACA,CONHN (FIG. 4A); (5,3)D HACACONHN and (5,3)D HACA,CO NHN (FIG. 4B); and (4,3)D CBCACONHN and (4,3)D CBCA,CO NHN (FIG. 4C). INEPT-type polarization transfers (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) are indicated by arrows, and Lxc3x6hr""s xe2x80x9cen passantxe2x80x9d frequency labeling module is indicated by a double arrow. The nuclei for which the chemical shift is detected in quadrature are shown in bold and are underlined. The nuclei with a grey background are simultaneously sampled in the GFT NMR dimension, and the chemical shifts of the boxed nuclei are used to establish sequential connectivities. In FIG. 4B, the chemical shifts of nitrogen spins shown in circles are measured is a separate dimension.
FIGS. 5A-G illustrate magnetization transfer pathways generating the basic spectra of GFT NMR experiments: (i) (4,3)D HNNCACBCA (FIG. 5A), (ii) (4,3)D HNN(CO)CACBCA and (4,3)D CBCACA(CO)NHN (FIG. 5B), (iii) (5,3)D HBHACBCACA(CO)NHN (FIG. 5C), (iv) (5,3)D HCC,CH-COSY (FIG. 5D), (v) (5,3)D HBCBCGCDHD (FIG. 5E), (vi) (4,2) HCC,CH-COSY (FIG. 5F), and (vii) (5,2)D HCCCH-COSY (FIG. 5G). In experiments (iv) and (vi), only magnetization transfer pathways corresponding to cross peaks in a 4D HCCH-COSY are shown. In experiment (vii), only the magnetization transfer pathway corresponding to cross peaks in a relayed 5D HCCCH-COSY is shown. INEPT-type polarization transfer are indicated by double arrows for xe2x80x9cout-and-backxe2x80x9d type experiments and single arrows for xe2x80x9cout-and-stayxe2x80x9d type experiments. The nucleus for which the chemical shift is detected in quadrature in all spectra constituting the GFT NMR experiment is underlined. The nuclei with grey background are simultaneously sampled in a single GFT NMR dimension, and the chemical shifts of the boxed nuclei are measured in the direct dimension. The chemical shifts of nitrogen spins (shown in circles) are measured in a separate dimension in experiments (i), (ii), and (iii), and the chemical shifts of 13Cxcex4 and 13Cicoupled (shown in circles) are measured in a separate dimension in experiments (iv) and (v), respectively. The double headed arrows between 13Cxcex1 and 13Cxcex2 in experiments (i), (ii), and (iii) indicate that the chemical shifts of 13Cxcex1/xcex2 [and 1Hxcex1/xcex2 in (iii)] first evolve independently, prior to transferring to 13Cxcex1 for frequency labeling.
FIG. 6 illustrates the rf pulse sequence used to record the (5,2)D HACACONHN GFT NMR experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no rf phase is marked, the pulse is applied along x. The high power 90xc2x0 pulse lengths were: 5.6 xcexcs for 1H and 15.3 xcexcs for 13C, and 39 xcexcs for 15N. Pulses on 13C prior to t1(13C) are applied at high power, and 13C decoupling during t1(1H) is achieved using a (90x-180y-90x) composite pulse (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford 1987), which is hereby incorporated by reference in its entirety). Subsequently, the 90xc2x0 and 180xc2x0 pulse lengths of 13Cxcex1 are adjusted to 51.6 xcexcs and 46 xcexcs, respectively, to minimize perturbation of the 13CO spins (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety). The width of the 90xc2x0 pulses applied to 13CO pulse is 51.6 xcexcs and the corresponding 180xc2x0 pulses are applied with same power. A SEDUCE (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety) 180xc2x0 pulse with a length 252 xcexcs is used to decouple 13CO during t1. WALTZ16 (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple 15N (rf=1.78 kHz) during acquisition. The SEDUCE sequence (rf=1.0 kHz) is used for decoupling of 13Cxcex1 during the 15N chemical shift evolution period. The 1H rf carrier is placed at 4.78 ppm. The 13Cxcex1, 13Cxe2x80x2 and 15N rf carriers are set to 56.3 ppm, 174.3 and 119.3 ppm, respectively. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (1 ms, 24 G/cm); G4 (250 xcexcs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 xcexcs, 8 G/cm); G8 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: xcfx841=1.6 ms, xcfx842=3.6 ms, xcfx843=4.4 ms, xcfx844=xcfx845=24.8 ms, xcfx846=5.5 ms, xcfx847=4.6 ms, xcfx848=1 ms. 1H-frequency labeling is achieved in a semi constant-time fashion with t1a (0)=1.79 ms, t1b (0)=1 xcexcs, t1c (0)=1.791 ms, xcex94t1a=62.5 xcexcs, xcex94t1b=32.9 xcexcs, xcex94t1c=29.6 xcexcs. Hence, the fractional increase of the semi constant-time period with t1 equals to xcex=1+xcex94t1c/xcex94t1a=0.53. Phase cycling: xcfx860=x; xcfx861=x, xe2x88x92x; xcfx862=x, x, xe2x88x92x, xe2x88x92x; xcfx863=x; xcfx864=4x,4(xe2x88x92x); xcfx866(receiver)=2(x,xe2x88x92x,xe2x88x92x,x). The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180xc2x0 shift of xcfx865. In case this enhancement scheme is not employed, quadrature detection is accomplished by altering the phase 4o according to States-TPPI (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996), which is hereby incorporated by reference in its entirety). For the setting of the phases xcfx860, xcfx861, xcfx862 and xcfx863 see Example 4.
FIGS. 7A-B depict the experimental scheme for the (5,2)D HACA,CONHN (FIG. 7A) and (4,3)D CBCA,CO NHN GFT NMR (FIG. 7B) experiments. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by filled and open vertical bars or shaped pulses, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high power 90xc2x0 pulse lengths were: 5.8 xcexcs for 1H and 15.4 xcexcs for 13C, and 38 xcexcs for 15N. In FIG. 7A, pulses on 13C prior to t1(13C) are applied at high power, and 13C decoupling during t1(1H) is achieved using a (90x-180y-90x) composite pulse (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety). Subsequently, the 90xc2x0 and 180xc2x0 pulse lengths of 13Cxcex1 are adjusted to 51.5 xcexcs and 46 xcexcs, respectively, to minimize perturbation of the 13CO spins. The width of the 90xc2x0 pulses applied to 13CO pulse is 52 xcexcs and the corresponding 180xc2x0 pulses are applied with same power. A SEDUCE (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) 180xc2x0 pulse with a length 252 xcexcs is used to decouple 13CO during t1(13Cxcex1). WALTZ16 (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple 15N (rf=1.78 kHz) during acquisition. The SEDUCE sequence (rf=1.0 kHz) is used for decoupling of 13Cxcex1 during the 15N chemical shift evolution period. The 1H rf carrier is placed at 4.78 ppm. The 13Cxcex1 and 15N rf carriers are set to 56.3 ppm and 119.3 ppm, respectively. All 13Cxe2x80x2 pulses are laminar shifted (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) by 118 ppm relative to the 13Cxcex1 carrier position. By setting the spectral width of the jointly sampled dimension to one half of 118 ppm, the apparent carrier position for sampling of 13Cxe2x80x2 chemical shift (174.3 ppm) is folded on the position of the 13Cxcex1 carrier position at 56.3 ppm. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (1 ms, 24 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 xcexcs, 8 G/cm); G8 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: xcfx841=1.6 ms, xcfx842=9.0 ms, xcfx844=11.0 ms, xcfx845=22.0 ms, xcfx846=5.5 ms, xcfx847=4.6 ms, xcfx848=1 ms. 1H-frequency labeling is achieved in a semi constant-time fashion with t1a (0)=1.7 ms, t1b (0)=1 xcexcs, t1c (0)=1.701 ms, xcex94t1a=60 xcexcs, xcex94t1b=35.4 xcexcs, xcex94t1c=xe2x88x9224.6 xcexcs. Hence, the fractional increase of the semi constant-time period with t1 equals to xcex=1+xcex94t1c/xcex94t1a=0.58. Phase cycling for artefact suppression: xcfx860=x; xcfx861=x, xe2x88x92x; xcfx862=x, x, xe2x88x92x, xe2x88x92x; xcfx863=x; xcfx864=4x, 4(xe2x88x92x); xcfx865=x; xcfx866=xcfx867=x; xcfx868(receiver)=2(x,xe2x88x92x,xe2x88x92x,x). Phases xcfx866 and xcfx867 are shifted by 500 to compensate for non-resonance effects. GFT NMR super phase-cycling for recording the 8 basic spectra: xcfx861=x,y; xcfx862=2x,2y; xcfx863=4x,4y (the G-matrix required for time domain editing is shown in equation 15 in Example 5). For acquisition of central peaks derived from 13C steady state magnetization, a second set of data sets with a 180xc2x0 shift for xcfx863 is collected and data are xe2x80x9cpre-processedxe2x80x9d as described (see equations 13 and 14 in Example 5). For second order central peak detection, the 1Hxcex1 and 13Cxcex1 chemical shift evolution periods are omitted and xcfx861=x,y; xcfx862=x; xcfx863=x. Third order central peaks were detected in 2D [15N, 1H]-HSQC (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety). (The G-matrices required for the central peak spectra are shown in equations 16-18 in Example 5). The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180xc2x0 shift of xcfx865. For implementation of (5,3)D HACA,CONHN, t1(15N) is replaced by t2(15N), and quadrature detection in t1 is accomplished by altering the phase xcfx86I according to States-TPPI. GFT NMR super phase cycle for the 4 basic spectra: xcfx862=x,y; xcfx863=2x,2y (the G-matrix required for time domain editing is shown in equation 16 of Example 5). First order central peaks are derived from 13C magnetization and are obtained by acquiring a second set of data sets with a 180xc2x0 shift for xcfx863. For second order central peak detection, t1(1Hxcex1) and t1(13Cxcex1) are omitted. (The G-matrices required for time domain editing of the central peak spectra are shown in equations 17 and 18 of Example 5). In FIG. 7B, pulses on 13C prior to t1(13C) are applied at high power. Subsequently, the 90xc2x0 and 180xc2x0 pulse lengths applied for 13Cxcex1/xcex2 are adjusted to 47.5 xcexcs and 42.5 xcexcs, respectively, to minimize perturbation of 13CO spins. The width of the 90xc2x0 pulses applied to 13CO pulse is 52 xcexcs and the corresponding 180xc2x0 pulses are applied with same power. SEDUCE 180xc2x0 pulses of 200 xcexcs pulse length are used to decouple 13CO during t1 and xcfx844. WALTZ16 is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers, as well as to decouple 15N (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of 13Cxe2x80x2 during the 15N chemical shift evolution period (rf=1.0 kHz). The 1H rf carrier is placed at 4.78 ppm. Initially, the 13C and 15N rf carriers are set to 41.3 ppm and 119.3 ppm, respectively. The 13Cxe2x80x2 carrier position is folded from 174.3 to 41.3 ppm by setting the spectral width in xcfx891 to one half of 133 ppm (=174.3 ppmxe2x88x9241.3 ppm). The 13C carrier is set to 56.3 ppm during the xcfx847 delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (250 xcexcs, 29.5 G/cm); G4 (250 xcexcs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 xcexcs, 8 G/cm); G8 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: xcfx840=1.7 ms, xcfx841=800 xcexcs, xcfx842=2.8 ms, xcfx84332 3.3 ms, xcfx844=6.6 ms, xcfx846=8.8 ms, xcfx847=24 ms, xcfx848=5.5 ms, xcfx840=4.6 ms, xcfx8410=1.0 ms. Phase cycling for artefact suppression: xcfx861=x; xcfx862=2(x), 2(xe2x88x92x); xcfx863=x; xcfx864=x, xe2x88x92x; xcfx865=xcfx866=xcfx867=xcfx868=x; xcfx869(receiver)=x,xe2x88x92x,xe2x88x92x,x. Phases xcfx866 and xcfx867 are shifted by 120xc2x0 to compensate for non-resonance effects. GFT NMR super phase-cycling for recording the two basic spectra: xcfx862=x,y (the G-matrix required for time domain editing is shown in equation 17 of Example 5). The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180xc2x0 shift of xcfx868. Quadrature detection in t1(13Cxe2x80x2) is accomplished by altering the phase xcfx866 according to States-TPPI (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety).
FIG. 8 depicts the experimental scheme for recording the (4,3)D CBCACONHN GFT NMR experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by filled and open vertical bars or shaped pulses, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high power 90xc2x0 pulse lengths were: 5.8 xcexcs for 1H and 15.4 xcexcs for 13C, and 38 xcexcs for 15N. Pulses on 13C prior to t1(13C) are applied at high power. Subsequently, the 90xc2x0 and 180xc2x0 pulse lengths applied for 13Cxcex1/xcex2 are adjusted to 47.5 xcexcs is and 42.5 xcexcs, respectively, to minimize perturbation of 13CO spins. The width of the 90xc2x0 pulse applied on 13CO pulse is 52 xcexcs and the corresponding 180xc2x0 pulses are applied with same power. A SEDUCE (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) 180xc2x0 pulse with a length of 200 xcexcs is used to decouple 13CO during t1 and xcfx844. The length of the spin-lock purge pulses SLx and SLy are 1.2 ms and 0.6 ms, respectively. WALTZ16 (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple 15N during acquisition (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of 13Cxcex1 during 15N evolution period (rf=1.0 kHz). The 1H rf carrier is placed at the water line at 4.78 ppm. Initially, the 13C and 15N rf carriers are set to 41.3 ppm and 119.3 ppm, respectively. The 13C carrier is set to 56 ppm during the second xcfx844/2 delay. The 13Cxe2x80x2 carrier position is set to 174.3 ppm. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (250 xcexcs, 29.5 G/cm); G4 (250 xcexcs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 xcexcs, 8 G/cm); G8 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. The delays are: xcfx841=800 xcexcs, xcfx842=3.1 ms, xcfx843=3.6 ms, xcfx84432 7.2 ms, xcfx845=4.4 ms, xcfx846=24.8 ms, xcfx847=24.8 ms, xcfx848=5.5 ms, xcfx849=4.6 ms, xcfx8410=1.0 ms. Phase cycling for artefact suppression: xcfx861=x; xcfx862=x,x,xe2x88x92x,xe2x88x92x; xcfx863=x, xe2x88x92x; xcfx864=x, xe2x88x92x; xcfx865=xe2x88x92x; xcfx866=x, x, xe2x88x92x, xe2x88x92x; xcfx867=x; xcfx868(receiver)=x, xe2x88x92x, xe2x88x92x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180xc2x0 shift of xcfx867 Quadrature detection in t1(13Cxe2x80x2) is accomplished by altering the phase xcfx864 according to States-TPPI. GFT NMR super phase-cycle for acquisition of the two basic spectra: xcfx862=x,y (the G-matrix required for time domain editing is shown in equation 17 of Example 5). For first order central peak detection an HNNCO pulse scheme (Cavanagh et al., Protein NMR spectroscopy, Wiley, New York (1996), which is hereby incorporated by reference in its entirety) is employed.
FIG. 9 depicts the experimental scheme for the (4,3)D HNNCACBCA experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high-power 90xc2x0 pulse lengths were: 6.0 xcexcs for 1H, 15.0 xcexcs for 13C and 42 xcexcs for 15N. The 90xc2x0 and 180xc2x0 pulse lengths applied on 13Cxcex1/xcex2 are adjusted to 40 xcexcs and 36 xcexcs, respectively, to minimize perturbation of 13CO spins. One lobe sinc pulses of duration 65 xcexcs were applied on 13CO with null at 13Cxcex1 to decouple 13CO from 13Cxcex1 spins during t1 and from 15N spins during t2. The selective 90xc2x0 1H pulse used to flip back the water magnetization is applied for 1.8 ms duration before the first 90xc2x0 pulse on 13Cxcex1. WALTZ16 is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple of 15N (rf=1.78 kHz) during acquisition. The 1H rf carrier is placed at the position of the solvent line at 4.78 ppm. The 13Cxcex1 and 15N carriers are set to 43.0 ppm and 120.9 ppm, respectively. The 13C carrier is switched to 56 ppm during the second t1 delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1.0 xcexcs, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (500 xcexcs, 29.5 G/cm); G5 (100 xcexcs, 16 G/cm); G4 (1.5 ms, 20 G/cm); G6(1.5 ms, 20 G/cm); G7 (1.25 ms, 30 G/cm); G8 (500 xcexcs, 8 G/cm); G9 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 xcexcs duration is inserted between a PFG pulse and an rf pulse. The delays have the following values: xcfx841=4.6 ms, xcfx842=5.4 ms, xcfx843=24 ms, xcfx844=24 ms, xcfx845=4.8 ms, xcfx84c=7.0 ms. Phase cycling: xcfx861=x, xe2x88x92x; xcfx862=y; xcfx863=x,x, xe2x88x92x, xe2x88x92x; xcfx864=x, xcfx865=4(x), 4(xe2x88x92x); xcfx866=x; xcfx867(receiver)=x, xe2x88x92x, xe2x88x92x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G7 is inverted in concert with a 180xc2x0 shift of xcfx866. Quadrature detection in t1(13Cxcex1) and t2(15N) is accomplished by altering the phases xcfx863 and xcfx864, respectively, according to States-TPPI. GFT-NMR super phase-cycling for recording the 2 basic spectra are: xcfx861=x,y; xcfx862=y,x.
FIG. 10 depicts the experimental scheme for the (4,3)D HNN(CO)CACBCA experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high-power 90xc2x0 pulse lengths were: 6.0 xcexcs for 1H, 15.0 xcexcs for 13C and 42 xcexcs for 15N. The 90xc2x0 and 180xc2x0 pulse lengths applied on 13Cxcex1/xcex2 are adjusted to 40 xcexcs and 36 xcexcs, respectively, to minimize perturbation of 13CO spins. One lobe sinc pulses of duration 65 xcexcs and with null at 13Cxcex1 were applied on 13CO to decouple from 13Cxcex1 spins during t1 and from 15N spins during t2. The 90xc2x0 pulse lengths for the one lobe sinc pulse on 13CO was 71 xcexcs. The selective 90xc2x0 1H pulse used to flip back the water magnetization is applied for 1.8 ms duration before the first 90xc2x0 pulse on 13Cxcex1. WALTZ16 is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple of 15N (rf=1.78 kHz) during acquisition. The 1H rf carrier is placed at the position of the solvent line at 4.78 ppm. The 13Cxcex1 and 15N carriers are set to 43 ppm and 120.9 ppm, respectively. The 13C carrier is switched to 56 ppm during the second t1 delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1.0 ms, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (1.0 ms, 29.5 G/cm); G4 (1.5 ms, 20 G/cm); G5 (100 xcexcs, 16 G/cm); G6(1.5 ms, 20 G/cm); G7 (1.25 ms, 30 G/cm); G8 (500 xcexcs, 8 G/cm); G9 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 xcexcs duration is inserted between a PFG pulse and an rf pulse. The delays have the following values: xcfx841=4.4 ms, xcfx842=5.4 ms, xcfx843=24 ms, xcfx844=24 ms, xcfx845=4.8 ms, xcfx84a=4.6 ms, xcfx84b=6.8 ms, xcfx84c=6.9 ms. Phase cycling: xcfx861=x, xe2x88x92x; xcfx862=y; xcfx863=x,x, xe2x88x92x, xe2x88x92x; xcfx864=x, xcfx865=4(x), 4(xe2x88x92x); xcfx866=x; xcfx867(receiver)=x, xe2x88x92x, xe2x88x92x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G7 is inverted in concert with a 180xc2x0 shift of xcfx866 Quadrature detection in t1(13C) and t2(15N) is accomplished by altering the phases xcfx863 and xcfx864, respectively, according to States-TPPI. GFT-NMR super phase-cycle for recording the 2 basic spectra are: xcfx861=x,y; xcfx862=y,x.
FIG. 11 depicts the experimental scheme for the (4,3)D CBCACA(CO)NHN experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high-power 90xc2x0 pulse lengths were: 5.9 xcexcs for 1H, 15.4 xcexcs for 13C, and 38 xcexcs for 15N. Pulses on 13C prior to t1(13C) are applied at high power, and 13C decoupling during t1(1H) is achieved using a (90x-180y-90x) composite pulse. Subsequently, the 90xc2x0 and 180xc2x0 pulse lengths applied for 13Cxcex1/xcex2 are adjusted to 47.5 xcexcs and 42.5 xcexcs, respectively, to minimize perturbation of 13CO spins. The width of the 90xc2x0 pulse applied on 13CO pulse is 52 xcexcs and the corresponding 180xc2x0 pulses are applied with same power. A SEDUCE 180xc2x0 pulse with a length of 200 xcexcs is used to decouple 13CO during t1 and xcfx844. The length of the spin-lock purge pulses SLx and SLy are 1.2 ms and 0.6 ms, respectively. WALTZ16 is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple 15N during acquisition (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of 13Cxcex1 during 15N evolution period (rf=1.0 kHz). The 1H rf carrier is placed at 4.78 ppm. Initially, the 13C and 15N r. f. carriers are set to 43 ppm and 120.9 ppm, respectively. The 13C carrier is set to 56 ppm before the first xcfx844/2 delay period. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (250 xcexcs, 29.5 G/cm); G4 (250 xcexcs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 xcexcs, 8 G/cm); G8 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 xcexcs duration is inserted between a PFG pulse and an rf pulse. The delays are: xcfx841=600 xcexcs, xcfx842=3.1 ms, xcfx843=3.35 ms, xcfx844=6.8 ms, xcfx845=4.4 ms, xcfx846=24.6 ms, xcfx847=24.6 ms, xcfx848=5.5 ms, xcfx849=4.6 ms, xcfx8410=1.0 ms. Phase cycling: xcfx861=x; xcfx862=x,x,xe2x88x92x,xe2x88x92x; xcfx863=x, xe2x88x92x; xcfx864=x, xe2x88x92x; xcfx865=x; xcfx866=x, x, xe2x88x92x, xe2x88x92x; xcfx867=x; xcfx868=x; xcfx869(receiver)=x, xe2x88x92x, xe2x88x92x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180xc2x0 shift of xcfx867. GFT-NMR super phase-cycling for recording the 2 basic spectra are: xcfx862=x,y. Quadrature detection in t1(13C) and t2(15N) is accomplished by altering the phases 48 and 45, respectively, according to States-TPPI.
FIG. 12 depicts the experimental scheme for the (5,3)D HBHACBCACA(CO)NHN experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The scaling factor K, for 1H chemical shift evolution during t1 is set to 1.0. The high-power 90xc2x0 pulse lengths were: 5.9 xcexcs for 1H, 15.4 xcexcs for 13C, and 38 xcexcs for 15N. Pulses on 13C prior to t1(13C) are applied at high power, and 13C decoupling during t1(1H) is achieved using a (90x-180y-90x) composite pulse. Subsequently, the 90xc2x0 and 180xc2x0 pulse lengths applied for 13Cxcex1/xcex2 are adjusted to 47.5 xcexcs and 42.5 xcexcs, respectively, to minimize perturbation of 13CO spins. The width of the 90xc2x0 pulse applied on 13CO pulse is 52 xcexcs and the corresponding 180xc2x0 pulses are applied with same power. A SEDUCE 180xc2x0 pulse with a length of 200 xcexcs is used to decouple 13CO during t1 and xcfx844. The length of the spin-lock purge pulses SLx and SLy are 1.2 ms and 0.6 ms, respectively. WALTZ16 is employed to decouple 1H (rf field strength=9.2 kHz) during the heteronuclear magnetization transfers as well as to decouple 15N during acquisition (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used for decoupling of 13Cxcex1 during 15N evolution period (rf=1.0 kHz). The 1H rf carrier is placed at xe2x88x921 ppm before the start of the semi constant time 1H chemical shift evolution period, and then switched to the water line at 4.78 ppm after the second 90xc2x0 1H pulse. Initially, the 13C and 15N r. f. carriers are set to 43 ppm and 120.9 ppm, respectively. The 13C carrier is set to 56 ppm during the second xcfx844/2 delay. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 xcexcs, 16 G/cm); G3 (250 xcexcs, 29.5 G/cm); G4 (250 xcexcs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, G/cm); G7 (500 xcexcms, 8 G/cm); G8 (125 xcexcs, 29.5 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 xcexcs duration is inserted between a PFG pulse and an rf pulse. The delays are: xcfx841=600 xcexcs, xcfx842=3.1 ms, xcfx843=3.35 ms, xcfx844=6.8 ms, xcfx845=4.4 ms, xcfx846=24.6 ms, xcfx847=24.6 ms, xcfx848=5.5 ms, xcfx849=4.6 ms, xcfx8410=1.0 ms. 1H-frequency labeling, at a 1H resonance frequency of 600 MHz is achieved in a semi constant-time fashion with t1a (0)=1.7 ms, t1b (0)=1 xcexcs, t1c (0)=1.701 ms, xcex94t1a=33.3 xcexcs, xcex94t1b=19.3 xcexcs, xcex94t1c=xe2x88x9214 xcexcs. Hence, the fractional increase of the semi constant-time period with t1 equals to k=1+xcex94t1c/xcex94t1a=0.58. Phase cycling: xcfx861=x; xcfx862=x,x,xe2x88x92x,xe2x88x92x; xcfx863=x, xe2x88x92x; xcfx864=x, xe2x88x92x; xcfx865=x; xcfx866=x, x, xe2x88x92x, xe2x88x92x; xcfx867=x; xcfx868=x; xcfx869(receiver)=x, xe2x88x92x, xe2x88x92x, x. The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated by reference in its entirety, is employed, i.e., the sign of G6 is inverted in concert with a 180xc2x0 shift of xcfx867. Quadrature detection in t1(13C) and t2(15N) is accomplished by altering the phases xcfx868 and xcfx865, respectively, according to States-TPPI. GFT-NMR super phase-cycling for recording the 4 basic spectra are: xcfx861=x,y; xcfx862=x,y. For acquisition of central peaks derived from 13C steady state magnetization, a second data set with he shifted by 180xc2x0, is collected.
FIG. 13 depicts the experimental scheme for the (5,3)D HCC,CH-COSY experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The scaling factor xcexa for 1H chemical shift evolution during t1 is set to 1.0. The high power 90xc2x0 pulse lengths were: 5.8 xcexcs for 1H and 15.4 xcexcs for 13C, and 38 xcexcs for 15N. The lengths of the 1H spin-lock purge pulses are: first SLx, 2.8 ms; second SLx, 1.7 ms; SLy: 4.9 ms. SEDUCE is used for decoupling of 13CO during t1 and t2 (rf field strength=1 kHz). WURST is used for decoupling of 13C during acquisition. The 1H carrier is placed at the position of the solvent line at 0 ppm before the start of the first semi constant time 1H evolution period, and then switched to the water line at 4.78 ppm after the second 90xc2x0 1H pulse. The 13C and 15N rf carriers are set to 43 ppm and 120.9 ppm, respectively. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (500 xcexcs, 6 G/cm); G2 (500 xcexcs, 11 G/cm); G3 (100 xcexcs, 12 G/cm); G4 (100 xcexcs, 12.5 G/cm); G5 (4.0 ms, 22 G/cm); G6 (500 xcexcs, 5 G/cm); G7 (3.0 ms, 22 G/cm); G8 (400 xcexcs, 6 G/cm). All gradients are applied along z-axis and are of rectangular shape. All PFG pulses are of rectangular shape. A recovery delay of at least 100 xcexcs duration is inserted between a PFG pulse and an rf pulse. The delays are: xcfx841=1.6 ms, xcfx842=750 xcexcs, xcfx843=2.65 ms, xcfx844=3.4 ms, xcfx845=6.8 ms, xcfx846=1.6 ms, xcfx847=2.4 ms, xcfx84a=350 xcexcs, xcfx84b=1.65 ms and xcfx84c=2.4 ms. Phase cycling: xcfx861=x; xcfx862=x, xe2x88x92x; xcfx863=x, xe2x88x92x; xcfx864=x; xcfx865=y; xcfx866(receiver)=x, xe2x88x92x. Quadrature detection in t1(13C/1H) and t2(13C) is accomplished by altering the phases xcfx864 and xcfx865, respectively, according to States-TPPI. Water suppression is accomplished by coherence pathway rejection using spin-lock purge pulses and pulsed field z-gradients. GFT-NMR super phase-cycle for recording the 4 basic spectra are: xcfx861=x,y; xcfx862=x,y. For acquisition of central peaks derived from 13C steady state magnetization, a second data set with 4) shifted by 180xc2x0 is collected.
FIG. 14 depicts the experimental scheme for the (5,3)D HBCBCGCDHD experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The scaling factor K for 1H chemical shift evolution during t1 is set to 1.0. The high power 90xc2x0 pulse lengths were: 5.8 xcexcs for 1H and 15.4 xcexcs for 13C. The first 180xc2x0 pulse on 13C prior to t1(13C) is applied at high power. Subsequently, the 90xc2x0 pulse lengths of 13Cxcex2 is adjusted to 66 xcexcs. The 180xc2x0 13Cxcex2 and 13Caro pulses are of gaussian-3 shape and 375 xcexcs duration. WALTZ16 is used for decoupling of 1H (rf field strength=4.5 kHz) during the magnetization transfer from 13Cxcex1 to 13Caro, and GARP is employed to decouple 13Caro (rf=2.5 kHz) during acquisition. The 1H rf carrier is placed at 4.78 ppm. The 13C rf carrier is set to 38 ppm during xcfx890(13C) and then switched to 135 ppm before the first 90xc2x0 pulse on 13Caro (pulse labeled with xcfx864). The 13C rf carrier is switched back to 125 ppm before the second 90xc2x0 pulse on 13Caro. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (500 xcexcs, 2 G/cm); G2 (1 ms, 22 G/cm); G3 (2 ms, 10 G/cm); G4 (500 xcexcs, 4 G/cm); G5 (1 ms, xe2x88x9214 G/cm); G6 (500 xcexcs, xe2x88x922 G/cm). All PFG pulses are of rectangular shape. A recovery delay of at least 100 xcexcs duration is inserted between a PFG pulse and an rf pulse. The delays are: xcfx841=1.8 ms, xcfx842=8.8 ms, xcfx843=71 xcexcs, xcfx844=4.3 ms, xcfx845=2.1 ms, xcfx846=710 xcexcs, xcfx848=1.4 ms, xcfx847=2.5 ms. 1H-frequency labeling, at a 1H resonance frequency of 600 MHz is achieved in a semi constant-time fashion with t1(0)=1.7 ms, t1b (0)=1 82 s, t1c (0)=1.701 xcex94t1a=33.3 xcexcs, xcex94t1b=19.3 xcexcs, xcex94t1c=xe2x88x9214 xcexcs. Hence, the fractional increase of the semi constant-time period with t1 equals to xcex=1+xcex94t1c/xcex94t1a=0.58. Phase cycling: xcfx861=x; xcfx862=x; xcfx863=x, y, xe2x88x92x, xe2x88x92y; xcfx864=4(x), 4(xe2x88x92x); xcfx865=x; xcfx866 (receiver)=x, xe2x88x92x, x, xe2x88x92x, xe2x88x92x, Quadrature detection in t1(13Cxcex4) and t2(13Cxcex3) is accomplished by altering the phases xcfx864 and xcfx865, respectively, according to States-TPPI. Water suppression is accomplished by presaturation of the water line during the relaxation delay and coherence pathway rejection using spin-lock purge pulses and pulsed field z-gradients. GFT-NMR super phase-cycling for recording the 4 basic spectra are: xcfx861=x,y; xcfx862=x,y. For acquisition of central peaks derived from 13C steady state magnetization, a second data set with xcfx861 shifted by 180xc2x0 is collected.
FIG. 15 depicts the experimental scheme for the (4,2)D HCCH-COSY experiment. Rectangular 90xc2x0 and 180xc2x0 pulses are indicated by thin and thick vertical bars, respectively, and phases are indicated above the pulses. Where no radio-frequency (rf) phase is marked, the pulse is applied along x. The high power 90xc2x0 pulse lengths were: 5.8 xcexcs for 1H and 15.4 xcexcs for 13C, and 38 xcexcs for 15N. The lengths of the 1H spin-lock purge pulses are: first SLx, 2.8 ms; second SLx, 1.7 ms; SLy: 4.9 ms. SEDUCE is used for decoupling of 13CO during t1 and t2 (rf field strength=1 kHz). WURST is used for decoupling of 13C during acquisition. The 1H carrier is placed at 4.78 ppm. The 13C and 15N rf carriers are set to 43 ppm and 120.9 ppm, respectively. The duration and strengths of the pulsed z-field gradients (PFGs) are: G1 (500 is, 6 G/cm); G2 (500 is, 11 G/cm); G3 (100 xcexcs, 12 G/cm); G4 (100 xcexcs, 12.5 G/cm); G5 (4 ms, 22 G/cm); G6 (500 xcexcs, 5 G/cm); G7 (3 ms, 30 G/cm); G8 (400 xcexcs, 6 G/cm). All gradients are applied along z-axis and are of rectangular shape. All PFG pulses are of rectangular shape. A recovery delay of at least 100 xcexcs duration is inserted between a PFG pulse and an rf pulse. The delays are: xcfx841=1.6 ms, xcfx842=750 xcexcs, xcfx843=2.65 ms, xcfx844=3.4 ms, xcfx845=6.8 ms, xcfx846=0.7 ms, xcfx847=3.2 ms. Phase cycling: xcfx861=x; xcfx862=x, xe2x88x92x; xcfx863=x, xe2x88x92x; xcfx864=x; xcfx865=y; xcfx866(receiver)=x, xe2x88x92x. Quadrature detection in t1(13C) is accomplished by altering the phases xcfx864 according to States-TPPI. Water suppression is accomplished by coherence pathway rejection using spin-lock purge pulses and pulsed field z-gradients. GFT-NMR super phase-cycle for recording the 4 basic spectra are: xcfx861=x,y; xcfx862=x,y. For acquisition of central peaks derived from 13C steady state magnetization, a second data set with xcfx861 shifted by 180xc2x0 is collected.
FIGS. 16A-B show the xcfx891[(15N;13Cxe2x80x2, 13Cxcex1, 1Hxcex1), xcfx892(1HN)]-, [xcfx891(15N;13Cxe2x80x2, 13Cxcex1), xcfx892(1HN)]-, [xcfx891(15N;13Cxe2x80x2), xcfx892(1HN)]-, and [xcfx891(15N), xcfx892(1HN)]-strips taken from the (5,2)D HACACONHN GFT NMR experiment (see FIG. 17). The signals were detected on the amide proton chemical shift of Ser 20. FIG. 16A shows spectra A1-A 15 containing the chemical shift multiplets. FIG. 16B shows spectra B1-B15 containing the individual edited chemical shift multiplet components. Note that when compared with FIG. 2 the order of the chemical shift multiplets appears to have changed. However, this is because xcfx891(1Hxcex1) less than 0 ppm (i.e., upfield relative to the carrier position) for Ser 20, and xcfx891(13Cxe2x80x2), xcfx891(13Cxcex1) and xcfx891(15N)  greater than 0 ppm (i.e, downfield relative to the respective carrier position). For simplicity, FIG. 2 was designed with the assumption that all resonances are located downfield to the respective carrier positions. The signals located at higher field in A15 and B15 arise from a side chain moiety and have thus no corresponding peaks in the other spectra (see also FIG. 17D). To facilitate the comparison of FIGS. 16A and 16B, the positions of multiplet components are indicated with thin lines.
FIGS. 17A-E show the 15 2D planes constituting the (5,2)D HACACONHN GFT NMR experiment (K=3) recorded for the 8.6 kDa protein ubiquitin. The linear combination of chemical shifts detected in a given plane is indicated. FIG. 17A shows the basic spectra B1 to B8. FIG. 17B shows the first order central peak spectra B9 to B12. FIG. 17C shows the second order central peak spectra B13 and B14. FIG. 17D shows the third order central peak spectrum B15. Signals arising from side chain moieties are in dashed boxes. FIG. 17E shows cross sections taken along xcfx891(15N;13Cxe2x80x2, 13Cxcex1, 1Hxcex1) at the peak of Ser 20 in B1 (at the top), along xcfx891(15N;13Cxe2x80x2, 13Cxcex1) in B9 (second from top), along xcfx891(15N;13Cxe2x80x2) in B13 (third from top), and along xcfx891(15N) in B15 (at the bottom). The sections are indicated in green in the corresponding panel. Comparison of sections from B1 and B9 shows that signals do not broaden with increasing K (FIG. 18), while the smaller line widths observed in spectra B13 to B15 result from longer tmax values (see Example 4). The 15 signals detected on the backbone amide proton of Ile 36 are circled. Doublets are observed in B1-B8 since Gly 35 exhibits non-degenerate 1Hxcex1 chemical shifts, yielding the correlation of six shifts: xcex4(1Hxcex12)=4.135xc2x10.006 ppm, xcex4(1Hxcex11)=3.929xc2x10.006 ppm, xcex4(13Cxcex1)=46.10xc2x10.019 ppm, xcex4(13Cxe2x80x2)=173.911xc2x10.017 ppm for Gly 35, and xcex4(15N)=120.295xc2x10.043 ppm and xcex4(1HN)=6.174xc2x10.005 ppm for Ile 36 (Table 2). The standard deviations of the indirectly detected chemical shifts were estimated from a Monte Carlo simulation (see description of FIG. 19). In accordance, the xcfx892(1HN) line width of the directly detected amid proton (20 Hz) was identified withxc2x13"sgr" (99.5% confidence interval) for locating the peak positions. Notably, phase sensitive editing of the chemical shift multiplets yields increasing peak dispersion (and thus resolution) in each of the constituent spectra compared to 2D [15N, 1H]-HSQC (panel B15). Nearly the same number of peaks is detected in each of 15 spectra, while the spectral width increases from SW1(15N)=1,440 Hz in B15 to SW1(15N/13Cxe2x80x2/13Cxcex1/1Hxcex1)=8,000 Hz in B1 . . . B8.
FIGS. 18A-C compare line widths and digital resolution of peaks detected in GFT and FT NMR. FIG. 18A shows (5,2)D HACACONHN GFT NMR: cross sections taken along xcfx891(15N;13Cxe2x80x2, 13Cxcex1, 1Hxcex1) at the peak of Ser 20 in spectrum B1 (at the top), along xcfx891(15N;13Cxe2x80x2, 13Cxcex1) in spectrum B9 (second from top), along xcfx891(15N;13Cxe2x80x2) in spectrum B13 (third from top), and along xcfx891(15N) in spectrum B15 (at the bottom). The same tmax value was chosen for all spectra in order to demonstrate that resonances do not broaden when increasing K from 0 to 3. FIG. 18B shows HACACONHN FT NMR: xcfx891(1Hxcex1), xcfx891(13Cxcex1), xcfx891(13Cxcex1), and xcfx891(15N) cross sections taken from 2D [xcfx891, xcfx892(1HN)]- planes obtained with the HACACONHN rf pulse scheme which were (i) recorded with the same tmax values and spectral widths, and (ii) were processed as (5,2)D HACACONHN. Comparison of FIG. 18A and FIG. 18B shows that the linewidth registered in the GFT NMR experiment equals the linewidth in the FT NMR experiment. FIG. 18C shows the same cross sections as in FIG. 18B are shown except that the planes were recorded and processed as a conventional 5D NMR spectrum would be [same maximal evolution times as in the basic spectra, 10(t1)*11(t2)*22(t3)*13(t4)*512(t5) complex points with spectral widths of SW1(15N)=1,440 Hz, SW2(13Cxe2x80x2)=1,500 Hz, SW3(13Cxcex1)=3,260 Hz, and SW4(1Hxcex1)=1,800 Hz and linear prediction to 20(t1)*22(t2)*32(t3)*26(t4)*512(t5) complex points]. This would yield a frequency domain data set of 32(xcfx891)*32(xcfx892)*32(xcfx893)*32(xcfx894)*512((xcfx895) real points of 2.1 GByte size as compared to 16.8 MByte for (5,2)D HACACONHN. Comparison with FIG. 18B and FIG. 18C makes the relatively poor resolution obtainable in 5D FT NMR apparent. Note that linear prediction and zero filling to 96(xcfx891)*96(xcfx892)*256(xcfx893)*128(xcfx894)*512(xcfx895) real points, which would be the closest match to the digital resolution obtained in (5,2)D HACACONHN, would result in an unrealistically large data size of 618 GByte.
FIG. 19 illustrates Monte-Carlo simulations performed to assess the increased precision of chemical shift measurements in (5,2)D HACACONHN GFT NMR. Standard deviations for the chemical shift measurements are plotted versus the number of spectra selected from the 15 2D spectra constituting this experiment (FIG. 17) in order to calculate the chemical shifts. "sgr"(1Hxcex1), "sgr"(13Cxcex1), "sgr"(13Cxe2x80x2) and "sgr"15N) represent the deviations for xcexa93(1Hxcex1), xcexa92(13C), xcexa91(13Cxe2x80x2) and xcexa90(15N) measurements, respectively. The following conservative statistical model is adopted. Line widths at half height, xcex94xcexd1/2, were measured along xcexa91 in (i) B1-B12 (basic spectra and first order central peaks) providing xcex94xcexd1/2(basic)=xcex94xcexd1/2(first)=60.1 Hz, (ii) B13 and B14 (second order central peaks) providing xcex94xcexd1/2(second)=38.2 Hz and (iii) B15 (third order central peaks) providing xcex94xcexd1/2(3rd)=28.1 Hz [FIG. 17E; these values are close to those expected from the tmax values obtained after linear prediction]. It is then assumed that the error for the identification of peak positions is associated with a Gaussian distribution, and that the Lorenzian line width, xcex94xcexd1/2, represents xc2x13"sgr" (99.5% confidence interval), i.e., xcex94xcexd1/2=6"sgr". xcex94xcexd1/2(basic) is equal to the line widths in the indirect dimensions of conventional FT NMR spectra recorded with the same maximal evolution time (FIGS. 17E and 18). Hence, "sgr"(basic) likewise represents the standard deviation obtained in FT NMR. Correspondingly are "sgr"(second)=xcex94xcexd1/2(second)/6 and "sgr"(third)=xcex94xcexd1/2(third)/6 the standard deviations for peak position identification in B13 and B14, and B15. The deviations "sgr"(1Hxcex1), "sgr"(13Cxcex1), "sgr"(13Cxe2x80x2) and "sgr"(15N) were obtained from Monte Carlo simulations of error propagation for which the following systems of equations were considered: (i) a minimal number of four out of the eight basic spectra (B1, B4, B6, B7; FIG. 20) (ii) B1-B8, (iii) B1-B12, (iv) B1-B14, or (v) B1-B15. Peak positions were randomly varied 10,000 times according to Gaussian distributions characterized by "sgr"(basic), "sgr"(second) and "sgr"(third). Subsequently, the systems of equations were solved using a least-squares fitting routine, and the deviations among the 10,000 solutions yielded "sgr"(1Hxcex1), "sgr"(13Cxcex1), "sgr"(13Cxe2x80x2) and "sgr"(15N). Note that "sgr"(1Hxcex1) is not further reduced when central peaks are involved since those do not encode xcexa9(1Hxcex1). Similarly, "sgr"(13Cxcex1) and "sgr"(13Cxe2x80x2) are not further reduced when second and third order central peaks are considered for calculation of chemical shifts. Notably, the standard deviations (labeled with an asterisk) obtained with four spectra critically depend on the particular selection (FIG. 20). The highest precision is obtained when choosing either B1, B4, B6 and B7, or B2, B3, B5 and B8 (FIGS. 20 and 17). The simulations are in neat agreement with calculations using the Gaussian law of error propagation (see FIG. 20).
FIGS. 20A-E show the results of Monte-Carlo simulations for the case that only four out of eight basic spectra of (5,2)D HACACONHN (FIG. 17A) are selected to calculate the chemical shifts. The standard deviations for the chemical shift measurements are plotted versus the number assigned to a particular combination. FIGS. 20A-D show "sgr"(15N), "sgr"(13Cxe2x80x2), "sgr"(13Cxcex1) and "sgr"(1Hxcex1), respectively, which represent the standard deviations for the measurement of the chemical shifts xcexa90(15N), xcexa91(13Cxe2x80x2), xcexa92(13Cxcex1) and xcexa93(1Hxcex1), respectively. FIG. 20E illustrates the assignment of numbers to the selections of four out of the 64 possible combinations       {                            (                                                    8                                                                    4                                              )                -        6            =                                                  (                              8                ·                7                ·                6                ·                5                            )                        /                          (                              4                ·                3                ·                2                ·                1                            )                                -          6                =        64              }    .
The six combinations which are subtracted from the binomial coefficient   "AutoLeftMatch"      (                            8                                      4                      )  
correspond to the cases where one of the three chemical shifts xcexa91, xcexa92 or xcexa93 is added to or subtracted from xcexa90 in all of the four selected spectra (i.e., no splitting is present among the four selected spectra which encodes the respective chemical shift). The spectra selected for a particular combination number are indicated as dots. The statistical model used for the Monte Carlo simulations is the same as described in the legend of FIG. 19.
FIGS. 21A-B show the composite plot of [xcfx891,xcfx892]-strips taken from (5,2)D HACA,CONHN (FIG. 21A) and HACACONHN data (FIG. 21B) collected for the 8.6 kDa protein ubiquitin with a total measurement time of 10.5 hours. The 2D data were acquired with 58(t1):512(t2) complex points and t1max(15N; 13Cxe2x80x2, 13Cxcex1, 1Hxcex1)=6.5 ms and t2max(1HN)=73.2 ms. In FIG. 21A, the strips were taken from basic spectra (B1 to B8), first order central peak spectra (B9 to B12), second order central peak spectra (B13 and B14) and third order central peak spectra (B15) and are centered about the amide proton chemical shift of Glu 64. The position of the backbone 15N chemical shift of Glu 64 is indicated by a dashed horizontal line, and the type of linear combination of chemical shifts detected for a given strip along xcfx891 is indicated at the top of the strip: B1 [xcexa90+xcexa91+xcexa92+xcexa93]; B2 [xcexa90xe2x88x92xcexa91+xcexa92+xcexa93]; B3 [xcexa90+xcexa91xe2x88x92xcexa92+xcexa93]; B4 [xcexa90xe2x88x92xcexa91xe2x88x92xcexa92+xcexa93]; B5 [xcexa90+xcexa91+xcexa92xe2x88x92xcexa93]; B6 [xcexa90xe2x88x92xcexa91+xcexa92xe2x88x92xcexa93]; B7 [xcexa90+xcexa91xe2x88x92xcexa92xe2x88x92xcexa93]; B8 [xcexa90xe2x88x92xcexa91xe2x88x92xcexa92xe2x88x92xcexa93]; B9 [xcexa90+xcexa91+xcexa92]; B10 [xcexa90xe2x88x92xcexa91+xcexa92]; B11 [xcexa90+xcexa91xe2x88x92xcexa92]; B12 [xcexa90xe2x88x92xcexa91xe2x88x92xcexa92]; B13 [xcexa90+xcexa91]; B14 [xcexa90xe2x88x92xcexa91]; B15 [xcexa90]. In FIG. 21 B, the corresponding strips are centered about the amide proton chemical shift of Ser 65. The variation of the 15 peaks relative to the 15N chemical shift of Ser 65 (indicated by a dashed horizontal line) matches the variation about the 15N chemical shift of Glu 64 in FIG. 21A. This allows one to establish the sequential connectivity between Glu 64 and Ser 65 based on the measurement of three chemical shifts, i.e., xcexa9(13Cxe2x80x2),xcexa9(13Cxcex1) and xcexa9(1Hxcex1). The shifts are obtained with high precision (Table 3) since the errors are reduced by the following factors when compared with FT NMR. For xcexa9(15N): √{square root over (15)}=3.9; xcexa9(13Cxe2x80x2): √{square root over (14)}=3.7; xcexa9(13Cxcex1): √{square root over (12)}=3.5; xcexa9(1Hxcex1): √{square root over (8)}=2.8. 1H and 13C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).
FIG. 22 shows the composite plot of [xcfx891,xcfx893]-strips taken from (5,3)D HACACONHN (strips labeled with xe2x80x98axe2x80x99) and (5,3)D HACA,CONHN data (strips labeled with xe2x80x98bxe2x80x99) collected for the 14 kDa NESG consortium target protein TT212 with a total measurement time of 60 hours. The 3D data were acquired with 56(t1):24(t2):512(t3) complex points and t1max(13Cxe2x80x2; 13Cxcex1, 1Hxcex1)=6.2 ms, t2max(15N)=16.4 ms and t3max(1HN)=73.2 ms. The first, second and third pair of strips in each block has been taken, respectively, at the 15N chemical shift of Ala 24, Ile 25 and Glu 26 along xcfx892(15N). The strips are centered about the corresponding amide proton shifts detected along xcfx893(1HN). The 15N shifts are given at the bottom of each pair of strips, which were taken from basic spectra (B1 to B4), the first order central peak spectra (B5 and B6) and the second order central peak spectra (B7). The type of linear combination of chemical shifts detected along xcfx891 is indicated at the top of the strips: B1 [xcexa90+xcexa91+xcexa92]; B2 [xcexa90xe2x88x92xcexa91+xcexa92]; B3 [xcexa90+xcexa91xe2x88x92xcexa92]; B4 [xcexa90xe2x88x92xcexa91xe2x88x92xcexa92]; B5 [xcexa90+xcexa91]; B6 [xcexa90xe2x88x92xcexa91]; B7 [xcexa90]. Sequential connectivities are indicated by horizontal lines and are established based on the measurement of three chemical shifts, i.e., xcexa9(13Cxe2x80x2), xcexa9(13Cxcex1), and xcexa9(1Hxcex1). The chemical shifts were obtained with high precision (Table 4), since the errors are reduced by the following factors when compared with FT NMR. For xcexa9(13Cxe2x80x2): √{square root over (7)}=2.6; xcexa9(13Cxcex1): √{square root over (4)}=2.4; xcexa9(1Hxcex1): √{square root over (4)}=2. 1H and 13C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).
FIG. 23 shows the composite plot of [xcfx891,xcfx893]-strips taken from (4,3)D CBCACONHN (strips labeled with xe2x80x98axe2x80x99) and (4,3)D CBCA,CONHN data (strips labeled with xe2x80x98bxe2x80x99) collected for the 8.6 kDa protein ubiquitin with a total measurement time of 11.2 hours. The 3D data were acquired with 60(t1):24(t2):512(t3) complex points and t1max(13Cxe2x80x2; 13Cxcex1/xcex2)=5.9 ms, t2max(15N)=17.2 ms and t3max(1HN)=73.2 ms. The first, second, and third pair of strips in each block has been taken, respectively, at the 15N chemical shift of Glu 64, Ser 65, and Thr 66 along xcfx892(15N). The strips are centered about the corresponding amide proton shifts detected along xcfx893(1HN). The 15N shifts are given at the bottom of each pair of strips, which were taken from basic spectra (B1 and B2) and the first order central peak spectra (B3). The type of linear combination of chemical shifts detected along xcfx891 is indicated at the top of the strips: B1 [xcexa90+xcexa91]; B2 [xcexa90xe2x88x92xcexa9]; B3 [xcexa90]. Sequential connectivities are indicated by horizontal lines and are established based on the measurement of three chemical shifts, i.e., xcexa9(13Cxe2x80x2),xcexa9(13Cxcex1) and xcexa9(13Cxcex2). [Since the 13Cxcex1/xcex2 carrier was set in between the 13Cxcex1, and 13Cxcex2chemical shift ranges (FIG. 7), one has that peaks at xcfx892(13Cxe2x80x2+13Cxcex1) and xcfx891(13Cxe2x80x2+13Cxcex2) in B1 appear in a xe2x80x9creversed orderxe2x80x9d when compared with B2, which exhibits peaks at xcfx892(13Cxe2x80x2xe2x88x9213Cxcex1) and xcfx893(13Cxe2x80x2xe2x88x9213Cxcex2).] The chemical shifts were obtained with high precision (Table 5) since the errors are reduced by the following factors when compared with FT NMR. For xcexa9(13Cxe2x80x2): √{square root over (3)}=1.7; xcexa9(13Cxcex1): √{square root over (2)}=1.4; xcexa9(13Cxcex2): √{square root over (2)}=1.4. 1H and 13C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).
FIG. 24 shows a composite plot of [xcfx891,xcfx893]-strips taken from (5,3)D HACACONHN (strips labeled with xe2x80x98axe2x80x99) and (5,3)D HACA,CONHN data (strips labeled with xe2x80x98bxe2x80x99) collected for ubiquitin with a total measurement time of 20.8 hours. The 3D data were acquired with 56(t1):24(t2):512(t3) complex points and t1max(13Cxe2x80x2; 13Cxcex1, 1Hxcex1)=6.2 ms, t2max(15N)=17.2 ms and t3max(1HN)=73.2 ms. The first, second, and third pair of strips in each block has been taken, respectively, at the 15N chemical shift of Lys 63, Glu 64, and Ser 65 along xcfx892(15N). The strips are centered about the corresponding amide proton shifts detected along xcfx893(1HN). The 15N shifts are given at the bottom of each pair of strips, which were taken from basic spectra (B1 to B4), the first order central peak spectra (B5 and B6) and the second order central peak spectra (B7). The type of linear combination of chemical shifts detected along xcfx891 is indicated at the top of the strips: B1 [xcexa90+xcexa91+xcexa92]; B2 [xcexa90xe2x88x92xcexa91+xcexa92]; B3 [xcexa90+xcexa91xe2x88x92xcexa92]; B4 [xcexa90xe2x88x92xcexa91xe2x88x92xcexa92]; B5 [xcexa90+xcexa91]; B6 [xcexa90xe2x88x92xcexa91]; B7 [xcexa90]. Sequential connectivities are indicated by horizontal lines and are established based on the measurement of three chemical shifts, i.e., xcexa9(13Cxe2x80x2),(13Cxcex1) and xcexa9(1Hxcex1). The chemical shifts were obtained with high precision (Table 6), since the errors are reduced by the following factors when compared with FT NMR. For xcexa9(13Cxe2x80x2):; xcexa9(13Cxcex1):; xcexa9(1Hxcex1):. 1H and 13C chemical shifts are in ppm relative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).
FIG. 25 shows the composite plot of [xcfx891(13Cxcex1; 13Cxcex1/xcex2), xcfx893(1HN)] strips taken from the basic spectra of (a) (4,3)D HNNCACBCA (B1a, B2a) and (b) (4,3)D HNN(CO)CACBCA (B1b, B2b). The [xcfx891(13Cxcex1), xcfx893(1HN)] strips taken from 3D HNNCA (B3a) and 4D HNN(CO)CA (B3b) spectra represent the first order central peaks for (4,3)D HNNCACBCA and (4,3)D HNN(CO)CACBCA, respectively. As an example, strips corresponding to xcexa92(15N) and xcexa93(1HN) chemical shifts for the residue Glu 73 of the 16 kDa protein ER75 are shown. Dashed lines connecting peaks establish sequential connectivities. Peaks labeled 1 to 9 in the figure correspond to the following linear combination of chemical shifts (ixe2x89xa1Glu 73; ixe2x88x921xe2x89xa1Ala 71):
1: xcexa90(13Cixe2x88x921xcex1)+xcexa91(13Cixe2x88x921xcex1);
2: xcexa90(13Cixcex1)+xcexa91(13Cixcex1)
3: xcexa90(13Cixcex1)+xcexa91(13Cixcex1), xcexa90(13Cixe2x88x921xcex1)+xcexa91(13Cixe2x88x921xcex1)
4: xcexa90(13Cixcex1)xe2x88x92xcexa91(13Cixcex1)
5: xcexa90(13Cixe2x88x921xcex1)xe2x88x92xcexa91(13Cixe2x88x921xcex1)
6: xcexa90(13Cixcex1)xe2x88x92xcexa91(13Cixcex2)
7: xcexa90(13Cixe2x88x921xcex1)xe2x88x92xcexa91(13Cixe2x88x921xcex2)
8: xcexa90(13Cixcex1) 
9: xcexa90(13Cixe2x88x921xcex1) 
FIG. 26 shows the composite plot of [xcfx891(13Cxcex1; 13Cxcex1/xcex2), xcfx893(1HN)] strips taken from the basic spectra of (a) (4,3)D CBCACA(CO)NHN (B1a and B2a) and (b) (4,3)D HNNCACBCA (B1b and B2b) illustrating how sequential resonance assignments along the polypeptide chain are obtained. As an example, the sequential walk for residues Val 27 to Ile 30 of the 7 kDa protein GR2 is shown. For simplicity, only the sequential connectivities inferred from the basic spectra are shown. The observed peak patterns are as described in FIG. 25.
FIG. 27 shows the composite plot of [xcfx891(13Cxcex1; 13Cxcex1/xcex2, 1Hxcex1/xcex2), xcfx893(1HN)] strips taken from the basic and first order central peak spectra of (5,3)D HBHACBCACA(CO)NHN (B1a, B2a, B3a and B4a). Note that [xcfx891(13Cxcex1; 13Cxcex1/xcex2), xcfx893(1HN)] strips taken from the basic spectra of (4,3)D CBCACA(CO)NHN (B5b and B6b) show the same peak patterns as those observed in the first order central peak spectra of (5,3)D HBHACBCACA(CO)NHN (B5a and B6a). As an example, strips corresponding to xcfx892(15N) and xcfx893(1HN) chemical shifts for Ile 30 of GR2 are shown. Peaks labeled 1 to 12 in the figure correspond to the following linear combination of chemical shifts for residue Ile 29:
1: xcexa90(13Cxcex1)+xcexa91(13Cxcex1)+xcexa92(1Hxcex1)
2: xcexa90(13Cxcex1)+xcexa91(13Cxcex2)+xcexa92(1Hxcex2)
3: xcexa90(13Cxcex1)+xcexa91(13Cxcex1)xe2x88x92xcexa92(1Hxcex1)
4: xcexa90(13Cxcex1)+xcexa91(13Cxcex2)xe2x88x92xcexa92(1Hxcex2)
5: xcexa90(13Cxcex1)xe2x88x92xcexa91(13Cxcex2)xe2x88x92xcexa92(1Hxcex2)
6: xcexa90(13Cxcex1)xe2x88x92xcexa91(13Cxcex1)xe2x88x92xcexa92(1Hxcex1)
7: xcexa90(13Cxcex1)xe2x88x92xcexa91(13Cxcex2)+xcexa92(1Hxcex2)
8: xcexa90(13Cxcex1)xe2x88x92xcexa91(13Cxcex1)+xcexa92(1Hxcex1)
9: xcexa90(13Cxcex1)xe2x88x92xcexa91(13Cxcex2)
10: xcexa90(13Cxcex1)xe2x88x92xcexa91(13Cxcex1)
11: xcexa90(13Cxcex1)+xcexa91(13Cxcex1)
12: xcexa90(13Cxcex1)+xcexa91(13Cxcex2)
FIG. 28 shows the composite plot of [xcfx891(13C; 13C, 1H), xcfx893(1H)] strips taken from the basic (B1-B4) and first order central peak (B5 and B6) spectra of (5,3)D HCC,CH-COSY. The [xcfx891(13C), xcfx893(1H)] strips taken from 3D (H)C,CHxe2x80x94COSY (B7) represents the second order central peak spectra of (5,3)D HCC,CH-COSY. As an example, strips corresponding to xcfx892(13Cxcex1) and xcfx893(1Hxcex1) chemical shifts for residue Ile 30 of GR2 are shown. Peaks shown in rectangular boxes correspond to cross peaks in a conventional 4D HCCH-COSY. Peaks labeled 1 to 13 correspond to the following linear combination of chemical shifts:
FIG. 29 shows the composite plot of [xcfx891(13Cxcex4; 13Cxcex2, 1Hxcex2), xcfx893(1Hxcex2)] strips taken from the basic (B1-B4) and first order central peak (B5 and B6) spectra of (5,3)D HBCBCGCDHD illustrating how resonance assignments for aromatic side-chain spins are obtained. The [xcfx891(13Cxcex4;13Cxcex2), xcfx893(1Hxcex4)] strips taken from 3D [13Cxcex4, 13Cxcex3, Hxcex4]-COSY represent the second order central peak spectra of (5,3)D HBCBCGCDHD. As an example, strips corresponding to xcfx892(13Cxcex3) and xcfx893(1Hxcex4) chemical shifts for His 68 of Ubiquitin are shown. Peaks labeled 1 to 7 correspond to the following linear combination of chemical shifts:
1: xcexa90(13Cxcex42)xe2x88x92xcexa91(13Cxcex2)xe2x88x92xcexa92(1Hxcex2)
2: xcexa90(13Cxcex42)xe2x88x92xcexa91(13Cxcex2)+xcexa92(1Hxcex2)
3: xcexa90(13Cxcex42)+xcexa91(13Cxcex2)+xcexa92(1Hxcex2)
4: xcexa90(13Cxcex42)+xcexa91(13Cxcex2)xe2x88x92xcexa92(1Hxcex2)
5: xcexa90(13Cxcex42)xe2x88x92xcexa91(13Cxcex2)
6: xcexa90(13Cxcex42)+xcexa91(13Cxcex2)
7: xcexa90(13Cxcex42)
FIG. 30 shows the composite plot of [xcfx891(13C; 13C, 1H), xcexa92(1H)] strips taken from the basic (B1-B4) and first order central peak (B5 and B6) spectra of (4,2)D HCCH-COSY spectra illustrating how resonance assignments for aromatic side-chain spins are obtained. The [xcfx891(13C), xcfx892(1H)] strip taken from 2D [13C-1H] HSQC (B7) represents the second order central peak spectra for (4,2)D HCCH-COSY. As an example, strips corresponding to xcfx892(Hxcex4) chemical shift for residue Tyr 59 of the 8.6 kDa protein Ubiquitin are shown. Peaks shown in rectangular boxes correspond to cross peaks in the conventional 4D HCCH-COSY. Peaks labeled 1 to 15 correspond to the following linear combination of chemical shifts:
The present invention provides an NMR data acquisition scheme which is based on the phase sensitive joint sampling of the indirect dimensions spanning a subspace of a conventional NMR experiment. This allows one to very rapidly obtain high dimensional NMR spectral information. Since the phase-sensitive joint sampling yields subspectra containing xe2x80x9cchemical shift multipletsxe2x80x9d, alternative data processing is required for editing the components of the multiplets. The subspectra are linearly combined using a so-called xe2x80x9cG-matrixxe2x80x9d and subsequently Fourier transformed. The chemical shifts are multiply encoded in the resonance lines constituting the shift multiplets. This corresponds to performing statistically independent multiple measurements, and the chemical shifts can thus be obtained with high precision. To indicate that a combined G-matrix and FT is employed, the new approach is named xe2x80x9cGFT NMR spectroscopyxe2x80x9d.
In GFT NMR spectroscopy, the chemical shift evolution periods spanning a given multidimensional subspace of an FT NMR experiment are xe2x80x9cjointlyxe2x80x9d sampled (FIG. 1). Thereby, the dimensionality N of an FT NMR spectrum can be adjusted to a given target dimensionality, Nt, by combined sampling of K+1 chemical shifts xcexa90, xcexa91, . . . xcexa9K encoded in K+1 indirect dimensions of the ND FT NMR experiment (K=Nxe2x88x92N,). Assuming that xcexa90 is detected in quadrature (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) and that the setting of the phases xc3x8j of the radiofrequency pulses exciting the spins of dimensions (j=1 . . . K) ensures cosine modulation, the transfer amplitude (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety) of the NtD experiment is proportional to       ⅇ          ⅈ      ⁢              xe2x80x83            ⁢                        Ω          ⁢                      xe2x80x83                          0            ⁢      t        ·            ∏              j        =        1            K        ⁢          xe2x80x83        ⁢                  cos        ⁡                  (                                    Ω              j                        ⁢            t                    )                    .      
The resulting peak centered around xcexa90 contains 2K components and is designated a xe2x80x9cchemical shift multipletxe2x80x9d (FIG. 2).
A shift of xc3x8j by 90xc2x0 yields a sin(xcexa9jt) instead of a cos(xcexa9jt) modulation, (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety), and 2K NtD spectra are recorded if all phases Ok are systematically varied between 0xc2x0 and 90xc2x0 (FIG. 1). In turn, a linear combination of these 2K spectra allows for the editing of the chemical shift multiplet components (FIG. 2). For brevity, cj=cos(xcexa9jxc2x7t), sj=sin(xcexa9jxc2x7t), and eixcexa9jt=eij are defined, so that       ⅇ          ⅈ      j        =                    c        j            +              i        ·                  s          j                      =                  [                  1          ⁢          i                ]            ·                        [                                                                      c                  j                                                                                                      s                  j                                                              ]                .            
With K=1, one obtains for the time evolution of the two shift multiplet components encoding sum and difference of xcexa90 and xcexa91.                                                         [                                                                                          ⅇ                                              j                        1                                                                                                                                                        ⅇ                                              -                                                  ⅈ                          1                                                                                                                                ]                        ⊗                          ⅇ                              j                0                                              =                    ⁢                                    ⅇ                              i                0                                      =                          [                                                                                                                  ⅇ                                                  ⅈ                          1                                                                    ·                                              ⅇ                                                  ⅈ                          1                                                                                                                                                                                                        ⅇ                                                  -                                                      ⅈ                            1                                                                                              ·                                              ⅇ                                                  ⅈ                          0                                                                                                                                ]                                                                    =                    ⁢                                    [                                                                                                                  [                                                  1                          ⁢                          i                                                ]                                            ⊗                                              [                                                  1                          ⁢                          i                                                ]                                                                                                                                                                                [                                                  1                          -                          i                                                ]                                            ⊗                                              [                                                  1                          ⁢                          i                                                ]                                                                                                        ]                        ·                          [                                                [                                                                                                              c                          1                                                                                                                                                              s                          1                                                                                                      ]                                ⊗                                  [                                                                                                              c                          0                                                                                                                                                              s                          0                                                                                                      ]                                            ]                                                                    =                    ⁢                                    [                                                [                                                                                                              1                          ⁢                          i                                                                                                                                                              1                          -                          i                                                                                                      ]                                ⊗                                  [                                      1                    ⁢                    i                                    ]                                            ]                        ·                          [                                                [                                                                                                              c                          1                                                                                                                                                              s                          1                                                                                                      ]                                ⊗                                  [                                                                                                              c                          0                                                                                                                                                              s                          0                                                                                                      ]                                            ]                                            "AutoRightMatch"
Accordingly, one obtains with K=2 for three chemical shifts xcexa90, xcexa91, and xcexa92:                     [                                                            ⅇ                                  ⅈ                  2                                                                                                        ⅇ                                  -                                      ⅈ                    2                                                                                      ]            ⊗              [                                                            ⅇ                                  ⅈ                  1                                                                                                        ⅇ                                  -                                      ⅈ                    1                                                                                      ]            ⊗              ⅇ                  ⅈ          o                      =                  [                              [                                                                                1                    ⁢                    i                                                                                                                    1                    -                    i                                                                        ]                    ⊗                      [                                                                                1                    ⁢                    i                                                                                                                    1                    -                    i                                                                        ]                    ⊗                      [                          1              ⁢              i                        ]                          ]            ·              [                              [                                                                                c                    2                                                                                                                    s                    2                                                                        ]                    ⊗                      [                                                                                c                    1                                                                                                                    s                    1                                                                        ]                    ⊗                      [                                                                                c                    0                                                                                                                    s                    0                                                                        ]                          ]              ,
and, in general, for K+1 chemical shifts xcexa90, xcexa91, . . . xcexa9K:             [                                                  ⅇ                              ⅈ                K                                                                                        ⅇ                              -                                  ⅈ                  K                                                                        ]        ⊗    …    ⊗          [                                                  ⅇ                              ⅈ                1                                                                                        ⅇ                              -                                  ⅈ                  1                                                                        ]        ⊗          ⅇ              ⅈ        o              =            [                        [                                                                      1                  ⁢                  i                                                                                                      1                  -                  i                                                              ]                ⊗        …        ⊗                  [                                                                      1                  ⁢                  i                                                                                                      1                  -                  i                                                              ]                ⊗                  [                      1            ⁢            i                    ]                    ]        ·          [                        [                                                                      c                  K                                                                                                      s                  K                                                              ]                ⊗        …        ⊗                  [                                                                      c                  1                                                                                                      s                  1                                                              ]                ⊗                  [                                                                      c                  0                                                                                                      s                  0                                                              ]                    ]      
The 2K dimensional complex vector on the left side of the equation is proportional to the vector {circumflex over (T)}c(K) comprising the desired edited spectra with the individual components of the chemical shift multiplets, that is,                     T        ^            c        ⁡          (      K      )        ∼            [                                                  ⅇ                              ⅈ                K                                                                                        ⅇ                              -                                  ⅈ                  K                                                                        ]        ⊗    …    ⊗          [                                                  ⅇ                              ⅈ                1                                                                                        ⅇ                              -                                  ⅈ                  1                                                                        ]        ⊗          ⅇ              ⅈ        o            
The 2K+1 dimensional real vector of the 2K+1 trigonometric modulations on the right side of the equation is proportional to the vector containing the spectra with the chemical shift multiplets in the real, Sjr, and imaginary parts, Sji, of the 2K NtD spectra (J=1 . . . 2K). Hence, with Ŝ(K)=[S1rS1iS2rS2i . . . S2KrS2Ki]T,             S      ^        ⁡          (      K      )        ∼            [                                                  c              K                                                                          s              K                                          ]        ⊗    …    ⊗          [                                                  c              1                                                                          s              1                                          ]        ⊗          [                                                  c              0                                                                          s              0                                          ]      
For the 2Kxc3x972K+1 complex G-matrix, which transforms Ŝ(K) into {circumflex over (T)}(K) according to the following equation (1):
{circumflex over (T)}c(K)32 Ĝc(K)19 Ŝ(K)xe2x80x83xe2x80x83(1)
one then obtains             G      c        ⁡          (      K      )        =      [                  [                                            1                                      i                                                          1                                                      -                i                                                    ]            ⊗              xe2x80x83            ⁢      …      ⁢              xe2x80x83            ⊗              [                                            1                                      i                                                          1                                                      -                i                                                    ]            ⊗              [                  1          ⁢                      xe2x80x83                    ⁢          i                ]              ]  
Alternatively, the multiplet components may be edited in the frequency domain (FIG. 2). The spectra of Ŝ(K) are Fourier transformed and a zero-order phase correction of nxc2x790xc2x0 is applied, depending on the number n of chemical shift sine modulations (see Example 1). The resulting real parts contain purely absorptive chemical shift multiplets and form the 2K dimensional real vector Â(K). Their linear combination yields the edited spectra contained in the 2K dimensional real vector according to the following equation (2):
{circumflex over (B)}(K)={circumflex over (F)}(K)xc2x7Â(K)xe2x80x83xe2x80x83(2)
Hence, {circumflex over (B)}(K) represents spectra which contain the edited 2K individual multiplet components at xcexa90xc2x1xcexa91xc2x1 . . . xcexa9K encoding the desired K+1 chemical shifts. {circumflex over (F)}(K) can be readily obtained from {circumflex over (F)}(Kxe2x88x921) by tensor product formation using the relation {circumflex over (F)}(K)={circumflex over (F)}=(Kxe2x88x921){circle around (X)}{circumflex over (F)}(1), with       F    ⁡          (      1      )        =      [                            1                          1                                      1                                      -            1                                ]  
for details and the relation between F and the G-matrix see Example 1).
The 2K spectra of {circumflex over (T)}c(K) and {circumflex over (B)}(K) are designated xe2x80x9cbasic spectraxe2x80x9d. Additional information is required to unambiguously derive all shift correlations of the parent ND experiment (which resolves degeneracy in up to Nxe2x88x921 dimensions) if two multiplets exhibit degenerate chemical shifts in all of the xe2x80x9cconventionallyxe2x80x9d sampled Ntxe2x88x921 dimensions. The acquisition of peaks defining the centers of the chemical shift splittings (xe2x80x9ccentral peaksxe2x80x9d) at the frequencies xcexa90+xcexa91xc2x1 . . . xc2x1xcexa9Kxe2x88x921, xcexa90xc2x1xcexa91xc2x1 . . . xcexa9Kxe2x88x922, . . . , xcexa90xc2x1xcexa91, and xcexa90 is then needed for identifying the components forming a given multiplet (FIG. 3A). Such xe2x80x9ccentral peak acquisitionxe2x80x9d has been introduced in the framework of the reduced-dimensionality NMR approach (Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002); Szyperski et al. J. Biomol. NMR. 3:127-132 (1993); Szyperski et al., J. Am. Chem. Soc. 115:9307-9308 (1993); Szyperski et al., J. Magn. Reson. B 105:188-191 (1994); Brutscher et al., J. Magn. Reson. B 105:77-82 (1994); Szyperski et al., J. Magn. Reson. B 108:197-203 (1995); Brutscher et al., J. Magn. Reson. B 109:238-242 (1995); Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996); Bracken et al., J. Biomol. NMR 9:94-100 (1997); Szyperski et al., J. Biomol NMR, 11:387-405 (1998); Astrof et al., J. Magn. Reson. 152:303-307 (2001); Xia et al., J. Biomol. NMR 24:41-40 (2002), which are hereby incorporated by reference in their entirety). The shift correlations of the ND spectrum can be obtained by xe2x80x9cbottom-upxe2x80x9d identification of the shift multiplets. This procedure essentially groups the peaks of the basic spectra into sets each belonging to one multiplet (FIG. 3). Because the basic peaks of two spin systems can be grouped even if central peaks overlap (FIG. 3B), this approach ensures that all correlations of the ND experiment are retained. GFT NMR (FIG. 1) thus requires one to record a total of   p  =                    ∑                  k          =          0                K            ⁢              xe2x80x83            ⁢              2        k              =                  2                  K          +          1                    -      1      
NtD spectra, including 2K basic spectra and 2Kxe2x88x921 central peak spectra. The p data sets constitute an xe2x80x9c(N,Nt)D GFT NMR experimentxe2x80x9d, and central peaks arising from omission of m chemical shifts are denoted to be of m-th order. For practical purposes, it is important to note that all components of a given multiplet have quite similar intensities since they are generated by multiple sine or cosine modulation of the transfer amplitude. Usually this does not hold for two peaks belonging to two different spin systems (FIG. 3A), because the nuclear spin relaxation times determining the peak intensities vary from spin system to spin system. Hence, inspection of peak intensities greatly facilitates the grouping of the peaks.
The joint sampling of several indirect dimensions reduces the minimal measurement time, Tm, of an (N,Nt)D GFT NMR experiment when compared with the parent ND FT experiment. The K+1 dimensions of an FT NMR spectrum exhibiting the spectral widths SW0, SW1, . . . , SWK are sampled with n0, n1, . . . nK complex points and yield maximal evolution times of t0,max, t1,max, . . . tK,max. In the (N,Nt)D GFT NMR experiment, the same maximal evolution times of the parent ND experiment can be realized by appropriate scaling of increments. (Szyperski et al. J. Biomol. NMR. 3:127-132 (1993); Szyperski et al., J. Magn. Reson. B 105:188-191 (1994), which are hereby incorporated by reference in their entirety). The acquisition of both cosine and sine modulated spectra for all jointly sampled chemical shifts (equation 1) corresponds to their phase-sensitive acquisition (Brutscher et al., J. Magn. Reson. B 109:238-242 (1995), which is hereby incorporated by reference in its entirety) and allows one to place the rf carrier positions in the center of the spectral ranges. Hence, the spectral width required for combined sampling is given by       SW    =                  ∑                  j          =          0                K            ⁢              xe2x80x83            ⁢                        κ          j                ·                  SW          j                      ,
where xcexaj represents the factor to scale (Szyperski et al. J. Am. Chem. Soc. 115:9307-9308 (1993); Szyperski et al., J. Magn. Reson. B 105:188-191 (1994), which are hereby incorporated by reference in their entirety) the sampling increments of the jth dimension to adjust maximal evolution times. If the same maximal evolution time is chosen for all dimensions and assuming, for simplicity, that delayed acquisition starts       at    ⁢          xe2x80x83        ⁢          1      /              SW        j              ,      n    =                  ∑                  j          =          0                K            ⁢              xe2x80x83            ⁢              n        j            
complex points are required to sample the resulting single dimension [if acquisition starts at t=0, one obtains that             n      =                        (                                    ∑                              j                =                0                            K                        ⁢                          xe2x80x83                        ⁢                          n              j                                )                -        K              ]    .
The ratio xcex5 of the minimal measurement time of an FT NMR experiment, Tm(FT), and the corresponding GFT NMR experiment, Tm(GFT), is then given by the number of FIDs that are required to sample the K+1 FT NMR dimensions divided by p times the number of FIDs required to sample the resulting single dimension:                     ϵ        =                                                            T                m                            ⁡                              (                FT                )                                                                    T                m                            ⁡                              (                GFT                )                                              =                                    (                                                2                  K                                /                                  (                                                            2                                              K                        +                        1                                                              -                    1                                    )                                            )                        ·                                          (                                                      ∏                                          j                      =                      0                                        K                                    ⁢                                      xe2x80x83                                    ⁢                                      n                    j                                                  )                            /                              (                                                      ∑                                          j                      =                      0                                        K                                    ⁢                                      xe2x80x83                                    ⁢                                      n                    j                                                  )                                                                        (        3        )            
This ratio scales with the product of the number of points over the corresponding sum and, thus, predicts large reductions in Tm (see Table 1 in Example 3; different ways to implement central peak acquisition as well as the impact of a particular implementation on xcex5 are described in Examples 2 and 3). (The GFT NMR scheme can be generalized by its M-fold application. Since this would involve M different G-matrices, such an experiment could be designated a GMFT NMR experiment. For example, two groups of dimensions can be identified with each group being combined to a single dimension. First an (N,Nxe2x80x2)D experiment is devised in which dimensions 1,2 . . . i are jointly sampled. Subsequently, the dimensionality of this experiment is to reduced to an (N,Nt) experiment by jointly sampling dimensions i+1, i+2, . . . K+2. For M projection steps, each invoking different sets of dimensions combined to a single one, the total reduction in minimal measurement time is then given by             ϵ      tot        =                  ∏                  j          =          1                M            ⁢              xe2x80x83            ⁢              ϵ        j              ,
where xcex5j is the reduction due to the j-th projection (equation 3)). The S/N of each of the 2K components in the basic spectra is reduced by (1/√{square root over (2)})K compared to the single peak in FT NMR. This is because each chemical shift splitting reduces the S/N by a factor of 2 relative to the FT NMR spectrum, while a factor of √{square root over (2)} is gained, because frequency discrimination is not associated with a FT (see FIG. 2: both cosine and sine modulated parts contribute equally to the signal intensity in the edited spectra) (The S/N ratio of FT NMR can be recovered by symmetrization about central peaks as described for reduced-dimensionality NMR (Szyperski et al., J. Magn. Reson. B 108:197-203 (1995), which is hereby incorporated by reference in its entirety) using the xe2x80x9cbottom upxe2x80x9d strategy employed for identification of shift multiplets (FIG. 3). Note that a reduced sensitivity is not relevant in the sampling limited regime.)
GFT NMR spectroscopy combines (i) multiple phase sensitive RD NMR, (ii) multiple xe2x80x98bottom-upxe2x80x99 central peak detection, and (iii) (time domain) editing of the components of the chemical shift multiplets. The resulting formalism embodies a flexible, generally applicable NMR data acquisition scheme. Provided that m=K+1 chemical shift evolution periods of an ND experiments are jointly sampled in a single indirect xe2x80x9cGFT dimensionxe2x80x9d, p=2mxe2x88x921 different (Nxe2x88x92K)D spectra represent the GFT NMR experiment containing the information of the parent ND experiment. Hence, such a set of p spectra is named an (N,Nxe2x88x92K)D GFT NMR experiment.
Thus, the present invention relates to a method of conducting a (N,Nxe2x88x92K) dimensional (D) G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiment, where N is the dimensionality of an N-dimensional (ND) Fourier transformation (FT) NMR experiment and K is the desired reduction in dimensionality relative to N. The method involves providing a sample and applying radiofrequency pulses for the ND FT NMR experiment to the sample. Then, m indirect chemical shift evolution periods of the ND FT NMR experiment are selected, where m equals K+1, and the m indirect chemical shift evolution periods are jointly sampled. Next, NMR signals detected in a direct dimension are independently cosine and sine modulated to generate (Nxe2x88x92K)D basic NMR spectra containing frequency domain signals with 2K chemical shift multiplet components, thereby enabling phase-sensitive sampling of all jointly sampled m indirect chemical shift evolution periods. Finally, the (Nxe2x88x92K) D basic NMR spectra are transformed into (Nxe2x88x92K) D phase-sensitively edited basic NMR spectra, where the 2K chemical shift multiplet components of the (Nxe2x88x92K) D basic NMR spectra are edited to yield (Nxe2x88x92K) D phase-sensitively edited basic NMR spectra having individual chemical shift multiplet components.
As described earlier, the (Nxe2x88x92K) D basic NMR spectra can be transformed into (Nxe2x88x92K) D phase-sensitively edited basic NMR spectra by applying a G-matrix defined as                     G        ^            ⁡              (        K        )              =          [                        [                                                    1                                            i                                                                    1                                                              -                  i                                                              ]                ⊗                  xe2x80x83                ⁢        …        ⁢                  xe2x80x83                ⊗                  [                                                    1                                            i                                                                    1                                                              -                  i                                                              ]                ⊗                  [                      1            ⁢                          xe2x80x83                        ⁢            i                    ]                    ]        ,
where i=√{square root over (xe2x88x921)}, under conditions effective to edit the chemical shift multiplet components in the time domain. Alternatively, the transforming can be carried out by applying a F-matrix defined as {circumflex over (F)}(K)={circumflex over (F)}(Kxe2x88x921){circle around (X)}{circumflex over (F)}(1), where                     F        ^            ⁡              (        1        )              =          [                                    1                                1                                                1                                              -              1                                          ]        ,
under conditions effective to edit the chemical shift multiplet components in the frequency domain.
In an alternate embodiment, the method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment can further involve selecting mxe2x80x2 indirect chemical shift evolution periods of the (Nxe2x88x92K)D FT NMR experiment, where mxe2x80x2 equals Kxe2x80x2+1. Then, the mxe2x80x2 indirect chemical shift evolution periods are jointly sampled. Next, NMR signals detected in a direct dimension are independently cosine and sine modulated to generate (Nxe2x88x92Kxe2x88x92Kxe2x80x2)D basic NMR spectra containing frequency domain signals with 2Kxe2x80x2 chemical shift multiplet components, thereby enabling phase-sensitive sampling of all jointly sampled mxe2x80x2 indirect chemical shift evolution periods. Finally, the (Nxe2x88x92Kxe2x88x92Kxe2x80x2) D basic NMR spectra are transformed into (Nxe2x88x92Kxe2x88x92Kxe2x80x2) D phase-sensitively edited basic NMR spectra, wherein the 2Kxe2x80x2 chemical shift multiplet components of the (Nxe2x88x92Kxe2x88x92Kxe2x80x2) D basic NMR spectra are edited to yield (Nxe2x88x92Kxe2x88x92Kxe2x80x2) D phase-sensitively edited basic NMR spectra having individual chemical shift multiplet components. The above-mentioned steps of selecting, jointly sampling, independently cosine and sine modulating, and transforming can be repeated one or more times, where mxe2x80x2 is modified for each repetition.
In an alternate embodiment, the method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment can further involve repeating one or more times the steps of selecting, jointly sampling, independently cosine and sine modulating, and transforming, where, for each repetition, the selecting involves selecting m-j indirect chemical shift evolution periods out of the m indirect chemical shift evolution periods, wherein j ranges from 1 to K, under conditions effective to generate 2K-j jth order central peak NMR spectra.
The method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment can also involve applying radiofrequency pulses of N-dimensional nuclear Overhauser enhancement spectroscopy (NOESY) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). Alternatively, the method can involve applying radiofrequency pulses of N-dimensional transverse relaxation optimized spectroscopy (TROSY) (Pervushin et al., Proc. Natl. Acad. Sci. USA, 94:12366-12371 (1997), which is hereby incorporated by reference in its entirety). In addition, the method can involve applying radiofrequency pulses so that spin-spin couplings are measured (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). The spin-spin couplings can be residual dipolar spin-spin coupling constants (Bax, Protein Sci., 12:1-16 (2003), which is hereby incorporated by reference in its entirety). The method can also involve applying radiofrequency pulses so that nuclear spin relaxation times are measured by sampling nuclear spin relaxation delays (Palmer, Annu. Rev. Biophys. Biomol. Struct., 30:129-155 (2001), which is hereby incorporated by reference in its entirety). The spin relaxation delays can be further jointly sampled with chemical shift evolution periods (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). In another embodiment, the jointly sampling the m indirect chemical shift evolution periods is achieved with a single continuous acquisition (Frydman et al., Proc. Natl. Acad. Sci., U.S.A., 99:15858-15862 (2002), which is hereby incorporated by reference in its entirety).
The present invention also discloses specific GFT NMR experiments and different combinations of those experiments which allows one to obtain sequential backbone chemical shift assignments for determining the secondary structure of a protein molecule and complete assignments of chemical shift values for a protein molecule including aliphatic and aromatic sidechain spin systems.
Specific GFT NMR Experiments
The present invention discloses the following six (N,Nxe2x88x92K)D GFT NMR experiments for the assignment of polypeptide backbone and 13Cxcex2 resonance: (i) with K=3, (5,2)D [HACACONHN] GFT NMR experiment and (5,2)D [HACA,CONHN] GFT NMR experiment for sequential assignment, (ii) with K=2, (5,3)D [HACA,CONHN GFT NMR experiment and (5,3)D [HACACONHN] GFT NMR experiment, where, in contrast to the (5,2)D experiments in (i), the 15N chemical shifts evolve separately, and (iii) with K=1, (4,3)D [CBCACONHN] GFT NMR experiment and (4,3)D [CBCA,CONHN] GFT NMR. The underlined letters indicate which chemical shifts that are jointly sampled. After G-matrix transformation, one obtains 23+1xe2x88x921=15 2D planes for the (5,2)D experiments (K=3), seven 3D spectra for the (5,3)D experiments (K=2) and three 3D spectra for the (4,3)D experiments (K=1). FIG. 4 illustrates the magnetization transfer pathways of the specific embodiments of these six GFT NMR experiments. (5,2)D [HACA,CONHN]/(5,2)D [HACACONHN] GFT NMR experiments and (5,3)D [HACA,CONH]/(5,3)D [HACACONHN] GFT NMR experiments correlate the backbone amide 15N and 1HN chemical shifts of residue i with the 13Cxe2x80x2, 13Cxcex1 and 1Hxcex1 chemical shifts of residue ixe2x88x921 and i, respectively, via one-bond scalar couplings (FIGS. 4A-B). In addition, the often smaller two-bond scalar couplings between the 15Ni and 13Cxcex1ixe2x88x921 may yield sequential connectivities in the HACA,CONHN experiments. The comma separating xe2x80x9cCAxe2x80x9d from xe2x80x9cCOxe2x80x9d indicates that the intraresidue 13Cxe2x80x2 chemical shift is obtained by creating two-spin coherence involving 13Cxe2x80x2 and 13Cxe2x80x2 during the intraresidue polarization transfer from 13Cxcex1 to 15N (Lxc3x6hr et al., J. Biomol. NMR 6:189-197 (1995), which is hereby incorporated by reference in its reference). (4,3)D [CBCACONHN] and (4,3)D [CBCA,CONHN] GFT NMR experiments correlate the backbone amide 15N and 1HN chemical shifts of residue i with the 13Cxe2x80x2, 13Cxcex1 and 13Cxcex2 chemical shifts of residue ixe2x88x921 and i, respectively, via one-bond scalar couplings (FIG. 4C), and the often smaller two-bond scalar couplings between the 15Ni and 13Cxcex1ixe2x88x921 may yield additional sequential connectivities in (4,3)D [CBCA,CONHN].
Thus, the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 3 to conduct a (5,2)D [HACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) an xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921; (2) an xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921; (3) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (4) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (5) a polypeptide backbone amide proton of amino acid residue i, 1HNI, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, and 15Ni, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, 15Ni). One specific embodiment of this method ((5,2)D HACACONHN) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 6.
The present invention also relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 3 to conduct a (5,2)D [HACA,CONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) an xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921; (2) an xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921; (3) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (4) a polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921; and (5) a polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, and 15Nixe2x88x921, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, 15Nixe2x88x921). One specific embodiment of this method ((5,2)D HACA,CONHN) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 7A.
Another aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) an xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921; (2) an xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921; (3) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (4) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (5) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921).
Yet another aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HACA,CONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, ixe2x88x921, and the chemical shift values for the following nuclei are measured: (1) an xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921; (2) an xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921; (3) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (4) a polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921; and (5) a polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1 Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921).
A further aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [CBCACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (3) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (4) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921 and 13Cxe2x80x2ixe2x88x9211 and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxe2x80x2ixe2x88x921). One specific embodiment of this method ((4,3)D CBCACONHN) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 8.
The present invention also relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [CBCA,CONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, ixe2x88x921, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (3) a polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921; and (4) a polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HN ixe2x88x921, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921 and 13Cxe2x80x2ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxe2x80x2ixe2x88x921). One specific embodiment of this method ((4,3)D CBCA,CONHN) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 7B.
In addition, the present invention discloses the following GFT NMR experiments for the assignment of polypeptide backbone and sidechain resonances: (i) (4,3)D [HNNCACBCA] GFT NMR experiment, (ii) (4,3)D [CBCACA(CO)NHN]/(4,3)D [HNN(CO)CACBCA] GFT NMR experiments, (iii) (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment, (iv) (5,3)D [HCC,CH-COSY] GFT NMR experiment, (v) (5,3)D [HBCBCGCDHD] GFT NMR experiment, (vi) (4,2)D [HCCH-COSY] GFT NMR experiment, and (vii) (5,2)D [HCCCH-COSY] GFT NMR experiment. Experiment (i) and (ii)/(iii) form pairs to sequentially assign backbone 13Cxcex1 and 13Cxcex2 resonances. Experiment (iii) also provides 1Hxcex1/xcex2 chemical shifts. The 13Cxcex1/xcex2 and 1Hxcex1/xcex2 chemical shifts, in turn, allow one to assign more peripheral spins of the aliphatic side-chain of a given amino acid residue using experiment (iv). Experiments (v) and (vi) can be used for resonance assignments of aromatic side-chain spins. The assignment of the side-chain chemical shifts can be further supported with experiment (vii). The magnetization transfer pathways of specific embodiments of these GFT NMR experiments (i)-(vii) are depicted in FIGS. 5A-G, respectively.
Thus, the present invention also relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [HNNCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residues i and ixe2x88x921, 13Cxcex1/xcex2i/ixe2x88x921; (2) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (3) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2i/ixe2x88x921 and 13Cxcex1i/ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2i/ixe2x88x921, 13Cxcex1i/ixe2x88x921). One specific embodiment of this method ((4,3)D HNNCACBCA) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 9.
In an alternate embodiment, the above method can be modified, where N equals 4 and K equals 2, to conduct a (4,2)D [HNNCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residues i and ixe2x88x921, 13Cxcex1/xcex2i/ixe2x88x921; (2) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (3) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2i/ixe2x88x921, 13Cxcex1i/ixe2x88x921, and 15Ni, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2i/ixe2x88x921, 13Cxcex1i/ixe2x88x921, 15Ni).
In another alternate embodiment, the above method can be modified, where N equals 4 and K equals 1 to conduct a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (3) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921 and 13Cxcex1ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921). One specific embodiment of this method ((4,3)D HNN(CO)CACBCA) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 10.
In yet another alternate embodiment, the above method can be modified, where N equals 4 and K equals 2 to conduct a (4,2)D [HNN(CO)CACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (3) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, and 15Ni; and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 15Ni).
In another alternate embodiment, the above method can be modified, where N equals 5 and K equals 2 to conduct a (5,3)D [HNNCOCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) (xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, (3) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (4) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921, (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921).
In yet another alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [HNNCOCACBCA] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, (3) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (4) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, and 15Ni; and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension,
Another aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 4 and K equals 1 to conduct a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (3) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 2 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921 and 13Cxcex1ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 2 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921). One specific embodiment of this method ((4,3)D CBCACA(CO)NHN) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 11.
In an alternate embodiment, the above method can be modified, where N equals 4 and K equals 2 to conduct a (4,2)D [CBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) (xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (3) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, and 15Ni, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 15Ni).
In another alternate embodiment, the above method can be modified, where N equals 5 and K equals 2 to conduct a (5,3)D [CBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) (xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, (3) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (4) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921, (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921).
In yet another alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [CBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two consecutive amino acid residues, ixe2x88x921 and i, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (2) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, (3) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (4) a polypeptide backbone amide proton of amino acid residue i, 1 HNi, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921 and 15Ni; (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, 15Ni).
Another aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and ixe2x88x921, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2-protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921; (2) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (3) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (4) a polypeptide backbone amide proton of amino acid residue i, HNi, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, and 13Cxcex1ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921). One specific embodiment of this method ((5,3)D HBHACBCACA(CO)NHN) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 12.
In an alternate embodiment, the above method can be modified, where N equals 6 and K equals 3 to conduct a (6,3)D [HBHACBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and ixe2x88x921, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2 protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921; (2) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (3) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (4) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (5) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 4 chemical shift evolution periods of the 6D FT NMR experiment, 1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x92l, and 13Cxe2x80x2ixe2x88x921, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921).
In another alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [HBHACBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and ixe2x88x921, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2 protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921; (2) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (3) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (4) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, and 15Ni, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 15Ni).
In yet another alternate embodiment, the above method can be modified, where N equals 6 and K equals 4 to conduct a (6,2)D [HBHACBCACACONHN] GFT NMR experiment. In this method, (a) the sample is a protein molecule having two amino acid residues, i and ixe2x88x921, and the chemical shift values for the following nuclei are measured: (1) xcex1- and xcex2 protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921; (2) xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921; (3) a polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921; (4) a polypeptide backbone amide nitrogen of amino acid residue i, 15Ni; and (5) a polypeptide backbone amide proton of amino acid residue i, 1HNi, (b) the selecting involves selecting 5 chemical shift evolution periods of the 6D FT NMR experiment, 1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, and 15Ni, and (c) the jointly sampling involves jointly sampling the 5 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex1/xcex2ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, 15Ni).
Yet another aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HCC,CH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton, 1H; (2) a carbon coupled to 1H, 13C; and (3) a carbon coupled to 13C, 13Ccoupled; and (4) a proton coupled to 13Ccoupled, 1Hcoupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1H, 13C, and 13Ccoupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1H, 13C, 13Ccoupled). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In one embodiment, the chemical shift evolution periods for 13C and 13Ccoupled can be correlated using total correlation spectroscopy (TOCSY) (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987), which is hereby incorporated by reference in its entirety). In another embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, 1Hi; (2) a carbon of amino acid residue i coupled to 1Hi, 13Ci; and (3) a carbon coupled to 13Ci, 13Cicoupled; and (4) a proton coupled with 13Cicoupled, 1Hicoupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1Hi, 13Ci, and 13Cicoupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1Hi, 13Ci, 13Cicoupled). One specific embodiment of this method ((5,3)D HCC,CH-COSY) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 13.
The present invention also relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 2 to conduct a (5,3)D [HBCBCGCDHD] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i, with an aromatic side chain, and the chemical shift values for the following nuclei are measured: (1) a xcex2-proton of amino acid residue i, 1Hxcex2i; (2) a xcex2-carbon of amino acid residue i, 13Cxcex2i; (3) a xcex3-carbon of amino acid residue i, 13Cxcex3i; (4) a xcex4-carbon of amino acid residue i, 13Cxcex4i; and (5) a xcex4-proton of amino acid residue i, 1Hxcex4i, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex2i, 13Cxcex2i, and 13Cxcex4i, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex2i, 13Cxcex2i, 13Cxcex4i). One specific embodiment of this method ((5,3)D HBCBCGCDHD) involves applying radiofrequency pulses for a 5D FT NMR experiment according to the scheme shown in FIG. 14.
In an alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,2)D [HBCBCGCDHD] GFT NMR experiment. In this method, (a) the sample is a protein molecule having an amino acid residue, i, with an aromatic side chain, and the chemical shift values for the following nuclei are measured: (1) a xcex2-proton of amino acid residue i, 1Hxcex2i; (2) a xcex2-carbon of amino acid residue i, 13Cxcex2i; (3) a xcex3-carbon of amino acid residue i; (4) a xcex4-carbon of amino acid residue i, 13Cxcex4i; and (5) a xcex4-proton of amino acid residue i, 1Hxcex4i, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, 1Hxcex2i, 13Cxcex2i, 13Cxcex3i, and 13Cxcex4i, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(1Hxcex2i, 13Cxcex2i, 13Cxcex3i, 13Cxcex4i).
Another aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 4 and K equals 2 to conduct a (4,2)D [HCCH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton, 1H; (2) a carbon coupled to 1H, 13C; (3) a carbon coupled to 13C, 13Ccoupled; and (4) a proton coupled to 13Ccoupled, 1Hcoupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, 1H, 13C, and 13Ccoupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1H, 13C, 13Ccoupled). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In one embodiment, the chemical shift evolution periods for 13C and 13Ccoupled are correlated using total correlation spectroscopy (TOCSY). In another embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, 1Hi; (2) a carbon of amino acid residue i coupled to 1Hi, 13Ci; (3) a carbon coupled to 13Ci, 13Cicoupled; and (4) a proton coupled to 13Cicoupled, 1Hicoupled, (b) the selecting involves selecting 3 chemical shift evolution periods of the 4D FT NMR experiment, 1Hi, 13Ci, and 13Cicoupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1Hi, 13Ci, 13Cicoupled). One specific embodiment of this method ((4,2)D HCCH-COSY) involves applying radiofrequency pulses for a 4D FT NMR experiment according to the scheme shown in FIG. 15.
Yet another aspect of the present invention relates to the above method of conducting a (N,Nxe2x88x92K)D GFT NMR experiment, where N equals 5 and K equals 3 to conduct a (5,2)D [HCCCH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton 1H; (2) a carbon coupled to 1H, 13C; (3) a carbon coupled to 13C, 13Ccoupled; (4) a carbon coupled to 13Ccoupled, 13Ccoupled-2; and (5) a proton coupled with 13Ccoupled-2, 1Hcoupled-2, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, H, 13C, 13Ccoupled, and 13Ccoupled-2 and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(1H, 13C, 13Ccoupled, 13Ccoupled-2). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In one embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, 1Hi; (2) a carbon of amino acid residue i coupled to 1Hi, 13Ci; (3) a carbon coupled to 13Ci, 13Cicoupled; (4) a carbon coupled to 13Cicoupled, 13Cicoupled2; and (5) a proton coupled with 13Cicoupled-2, 1Hicoupled-2, (b) the selecting involves selecting 4 chemical shift evolution periods of the 5D FT NMR experiment, 1Hi, 13Ci, 13Cicoupled and 13Cicoupled-2, and (c) the jointly sampling involves jointly sampling the 4 chemical shift evolution periods in an indirect time domain dimension, t1(1Hi, xe2x80x94Ci, 13Cicoupled, 13Cicoupled-2).
In an alternate embodiment, the above method can be modified, where N equals 5 and K equals 3 to conduct a (5,3)D [HCCCH-COSY] GFT NMR experiment. In this method, (a) the chemical shift values for the following nuclei are measured: (1) a proton, 1H; (2) a carbon coupled to 1H, 13C; (3) a carbon coupled to 13C, 13Ccoupled; (4) a carbon coupled to 13Ccoupled, 13Ccoupled-2; and (5)a proton coupled with 13Ccoupled-2, 1Hcoupled-2, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1H, 13C, and 13Ccoupled, and (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1H, 13C, 13Ccoupled). The sample in this method can be any molecule such as (metallo)-organic molecules and complexes, nucleic acid molecules such as DNA and RNA, lipids, or polymers. In another embodiment, (a) the sample is a protein molecule having an amino acid residue, i, and the chemical shift values for the following nuclei are measured: (1) a proton of amino acid residue i, 1Hi; (2) a carbon of amino acid residue i coupled to 1Hi, 13Ci; (3) a carbon coupled to 13Ci, 13Cicoupled; (4) a carbon coupled to 13Cicoupled, 13Cicoupled-2; and (5) a proton coupled with 13Cicoupled-2, 1Hicoupled-2, (b) the selecting involves selecting 3 chemical shift evolution periods of the 5D FT NMR experiment, 1Hi, 13Ci, and 13Cicoupled (c) the jointly sampling involves jointly sampling the 3 chemical shift evolution periods in an indirect time domain dimension, t1(1Hi, 13Cicoupled).
Combinations of GFT NMR Experiments
A set of multidimensional GFT NMR experiments enables one to devise strategies for GFT NMR-based (high throughput) resonance assignment of proteins or other molecules.
Thus, another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an xcex1-proton, 1Hxcex1 an xcex1-carbon, 13Cxcex1, a polypeptide backbone carbonyl carbon, 13Cxe2x80x2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1H, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,2)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921, the xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi and (2) a (5,2)D [HACA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921. Then, sequential assignments of the chemical shift values of 1Hxcex1, 13Cxcex1, 13Cxe2x80x2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,2)D [HACACONHN] GFT NMR experiment with the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,2)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921 (Wxc3xcthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as xcex1-helices and xcex2-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).
Yet another aspect of the present invention relates to a method for sequentially assigning chemical shift values of an xcex1-proton, 1Hxcex1, an xcex1-carbon, 13Cxcex1, a polypeptide backbone carbonyl carbon, 13Cxe2x80x2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1HN, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HACACONHN] GFT NMR experiment to measure and connect the chemical shift values of the xcex1-proton of amino acid residue ixe2x88x921, 1Hxcex1ixe2x88x921, the xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi and (2) a (5,3)D [HACA,CONHN]0 GFT NMR experiment to measure and connect the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921. Then, sequential assignments of the chemical shift values of 1Hxcex1, 13Cxcex1, 13Cxe2x80x2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,3)D [HACACONHN] GFT NMR experiment with the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 measured by the (5,3)D [HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, and 13Cxe2x80x2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921 (Wxc3xcthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as xcex1-helices and xcex2-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).
A further aspect of the present invention relates to a method for sequentially assigning chemical shift values of xcex1- and xcex2-carbons, 13Cxcex1/xcex2, a polypeptide backbone carbonyl carbon, 13Cxe2x80x2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1HN, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [CBCACONHN] GFT NMR experiment to measure and connect the chemical shift values of the xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, the polypeptide backbone carbonyl carbon of amino acid residue ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi and (2) a (4,3)D [CBCA,CONHN] GFT NMR experiment to measure and connect the chemical shift values of 13Cxcex1/xcex2ixe2x88x921, 13Cxe2x80x2ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, HNixe2x88x921. Then, sequential assignments of the chemical shift values of 13Cxcex1/xcex2, 13Cxe2x80x2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 and 13Cxe2x80x2ixe2x88x921 measured by the (4,3)D [CBCACONHN] GFT NMR experiment with the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 and 13Cxe2x80x2ixe2x88x921 measured by the (4,3)D [CBCA, CONHN] GFT NMR experiment, (ii) using the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 and 13Cxe2x80x2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921 (Wxc3xcthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR. 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as xcex1-helices and xcex2-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).
The present invention also relates to a method for sequentially assigning chemical shift values of xcex1- and xcex2-carbons, 13Cxcex1/xcex2, a polypeptide backbone amide nitrogen, 15N, and a polypeptide backbone amide proton, 1HN, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,3)D [HNNCACBCA] GFT NMR experiment to measure and connect the chemical shift values of the xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921, the xcex1-carbon of amino acid residue ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue ixe2x88x921, 15Nixe2x88x921, and the polypeptide backbone amide proton of amino acid residue ixe2x88x921, 1HNixe2x88x921 and (2) a GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of 13Cxcex1/xcex2ixe2x88x921, 13Cxcex1ixe2x88x921, the polypeptide backbone amide nitrogen of amino acid residue i, 15Ni, and the polypeptide backbone amide proton of amino acid residue i, 1HNi. Then, sequential assignments of the chemical shift values of 13Cxcex1/xcex2, 15N, and 1HN are obtained by (i) matching the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 measured by the GFT NMR experiment selected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment with the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 measured by the (4,3)D [HNNCACBCA] GFT NMR experiment, (ii) using the chemical shift values of 13Cxcex1/xcex2ixe2x88x921 to identify the type of amino acid residue ixe2x88x921 (Wxc3xcthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993), which are hereby incorporated by reference in their entirety), and (iii) mapping sets of sequentially connected chemical shift values to the amino acid sequence of the polypeptide chain and using the chemical shift values to locate secondary structure elements (such as xcex1-helices and xcex2-sheets) within the polypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which are hereby incorporated by reference in their entirety).
Another aspect of the present invention relates to a method for assigning chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain protons, 1Hxcex3/xcex4/xcex5, and chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain carbons located peripheral to xcex2-carbons, 13Cxcex3/xcex4/xcex5, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue ixe2x88x921, 1Hixe2x88x921, a carbon of amino acid residue ixe2x88x921 coupled to 1Hixe2x88x921, 13Cixe2x88x921, a carbon coupled to 13Cixe2x88x921, 13Cxcex1ixe2x88x921coupled, and a proton coupled to 13Cxe2x88x921coupled, 1HNixe2x88x921coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of xcex1- and xcex2-protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921, and xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921. Then, assignments of the chemical shift values of 1Hxcex3/xcex4/xcex5 and 13Cxcex3/xcex4/xcex5 are obtained by (i) identifying 1Hixe2x88x921, 13Cixe2x88x921, 13Cixe2x88x921coupled, and 1Hixe2x88x921coupled measured by the (5,3)D [HCC,CH-COSY] GFT NMR experiment as 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxcex2ixe2x88x921, and 1Hxcex2ixe2x88x921, respectively, and thereby matching the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 with the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 in conjunction with other chemical shift connections from the (5,3)D [HCC,CH-COSY] GFT NMR experiment to measure the chemical shift values of 1Hxcex3/xcex4/xcex5ixe2x88x921 and 13Cxcex3/xcex4/xcex5ixe2x88x921.
Yet another aspect of the present invention relates to a method for assigning chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain protons, 1Hxcex3/xcex4/xcex5, and chemical shift values of xcex3-, xcex4-, and xcex5-aliphatic sidechain carbons located peripheral to xcex2-carbons, 13Cxcex3/xcex4/xcex5, of a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (4,2)D [HCCH-COSY] GFT NMR experiment to measure and connect the chemical shift values of a proton of amino acid residue ixe2x88x921, 1Hixe2x88x921, a carbon of amino acid residue ixe2x88x921 coupled to 1Hixe2x88x921, 13Cixe2x88x921, a carbon coupled to 13Cixe2x88x921, 13C ixe2x88x921coupled, and a proton coupled to 13Cixe2x88x921coupled, 1Hixe2x88x921coupled, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of xcex1- and xcex2-protons of amino acid residue ixe2x88x921, 1Hxcex1/xcex2ixe2x88x921, and xcex1- and xcex2-carbons of amino acid residue ixe2x88x921, 13Cxcex1/xcex2ixe2x88x921. Then, assignments of the chemical shift values of 1Hxcex3/xcex4/xcex5 and 13Cxcex3/xcex4/xcex5 are obtained by (i) identifying 1Hixe2x88x921, 13Cixe2x88x921, 13Cixe2x88x921coupled, and 1HNixe2x88x921coupled measured by the (4,2)D [HCCH-COSY] GFT NMR experiment as 1Hxcex1ixe2x88x921, 13Cxcex1ixe2x88x921, 13Cxcex2ixe2x88x921, and 1Hxcex2ixe2x88x921, respectively, and thereby matching the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 with the chemical shift values of 1Hxcex1/xcex2ixe2x88x921 and 13Cxcex1/xcex2ixe2x88x921 measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shift values of 1Hxcex1/xcex2ixe2x88x921, and 13Cxcex1/xcex2ixe2x88x921 in conjunction with other chemical shift connections from the (4,2)D [HCCH-COSY] GFT NMR experiment to measure the chemical shift values of 1Hxcex3/xcex4/xcex5ixe2x88x921 and 13Cxcex3/xcex4/xcex5ixe2x88x921.
A further aspect of the present invention relates to a method for assigning chemical shift values of a xcex3-carbon, 13Cxcex3, a xcex4-carbon, 13Cxcex4, and a xcex4-proton, 1H5, of an amino acid residue containing an aromatic spin system in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a (5,3)D [HBCBCGCDHD] GFT NMR experiment to measure and connect the chemical shift values of a xcex2-proton of amino acid residue ixe2x88x921, 1Hxcex2ixe2x88x921, a xcex2-carbon of amino acid residue ixe2x88x921, 13Cxcex2ixe2x88x921, a xcex4-carbon of amino acid residue ixe2x88x921, 13Cxcex3ixe2x88x921, a xcex4-carbon of amino acid residue ixe2x88x921, 13Cxcex4ixe2x88x921, and a xcex4-proton of amino acid residue ixe2x88x921, 1Hxcex4ixe2x88x921, and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect the chemical shift values of 1Hxcex2ixe2x88x921 and 13Cxcex2ixe2x88x921. Then, assignments of the chemical shift values of 13Cxcex3, 13Cxcex4, and 1Hxcex4 are obtained by (i) matching the chemical shift values of 1Hxcex2ixe2x88x921 and 13Cxcex2ixe2x88x921 measured by the (5,3)D HBCBCACA(CO)NHN GFT NMR experiment with the chemical shift values of 1Hxcex2ixe2x88x921 and 13Cxcex2ixe2x88x921 measured by the (5,3)D [HBCBCGCDHD] GFT NMR experiment, and (ii) using the chemical shift values of 13Cxcex3, 13Cxcex4, and 1Hxcex4 to identify the type of amino acid residue containing the aromatic spin system.
The present invention also relates to a method for assigning chemical shift values of aliphatic and aromatic protons and aliphatic and aromatic carbons of an amino acid residue containing aliphatic and aromatic spin systems in a protein molecule. The method involves providing a protein sample and conducting a set of G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample including: (1) a first GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aliphatic spin system, to measure and connect the chemical shift values of xcex1- and xcex2-protons of amino acid residue i, 1Hxcex1/xcex2i, xcex1- and xcex2-carbons of amino acid residue i, 13Cxcex1/xcex2i, a xcex3-carbon of amino acid residue i, 13Cxcex3i, and (2) a second GFT NMR experiment, which is selected from the group consisting of a (5,3)D [HCC,CH-COSY] GFT NMR experiment, a (4,2)D [HCCH-COSY] GFT NMR experiment, a (5,2)D [HCCCH-COSY] GFT NMR experiment, and a (5,3)D [HCCCH-COSY] GFT NMR experiment and is acquired for the aromatic spin system, to measure and connect the chemical shift values of 13Cxcex3i and other aromatic protons and carbons of amino acid residue i. Then, assignments of the chemical shift values of the aliphatic and aromatic protons and aliphatic and aromatic carbons are obtained by matching the chemical shift value of 13Cxcex3i measured by the first GFT NMR experiment with the chemical shift value of 13Cxcex3i measured by the second GFT NMR experiment. In another embodiment, the set of GFT NMR experiments can be conducted by using 13Cxcex3steady state magnetization to generate first order central peaks.
The above-described methods for assigning chemical shift values in a protein molecule can involve further subjecting the protein sample to nuclear Overhauser enhancement spectroscopy (NOESY) (Wxc3xcthrich, NMR of Proteins and Nucleic Acids, Wiley, New York (1986), which is hereby incorporated by reference in its entirety), to NMR experiments that measure scalar coupling constants (Eberstadt et al., Angew. Chem. Int. Ed. Engl., 34:1671-1695 (1995); Cordier et al., J. Am. Chem. Soc., 121:1601-1602 (1999), which are hereby incorporated by reference in their entirety), or to NMR experiments that measure residual dipolar coupling constants (Prestegard, Nature Struct. Biol., 5:517-522 (1998); Tjandra et al., Science, 278:1111-1114 (1997), which are hereby incorporated by reference in their entirety), to deduce the tertiary fold or tertiary structure of the protein molecule.
Another aspect of the present invention relates to a method for obtaining assignments of chemical shift values of 1H, 13C, and 15N of a protein molecule. The method involves providing a protein sample and conducting five G matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments on the protein sample, where (1) a first experiment is a (4,3)D [HNNCACBCA] GFT NMR experiment for obtaining intraresidue correlations of chemical shift values; (2) a second experiment is a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment for obtaining interresidue correlations of chemical shift values; (3) a third experiment is a (5,3)D [HCC,CH-COSY] GFT NMR experiment for obtaining assignments of aliphatic sidechain chemical shift values; (4) a fourth experiment is a (5,3)D [HBCBCGCDHD] GFT NMR experiment for linking chemical shift values of aliphatic protons, 1Hxcex2 and 13Cxcex2, and aromatic protons, 13Cxcex4 and 1Hxcex4; and (5) a fifth experiment is a (4,2)D [HCCH-COSY] GFT NMR experiment for obtaining assignments of aromatic sidechain chemical shift values. These five GFT NMR experiments can be employed for obtaining nearly complete resonance assignments of proteins including aliphatic and aromatic side chain spin systems.